Properties we are going to use :
1. (a^m)^n = a^mn
2. a^m : a^n = a^(m-n)
((a^-2)^-1)^-1 = (a^(-2 x -1))^-1 = (a^2)^-1 = a^-2
(a : a^-1)^2 = (a^1 - (-1))^2 = (a^2)^2 = a^4
Therefore, the expression is simplified down to a^-2 : a^4
a^-2 : a^4 = a^(-2 - 4) = a^-6.
PLEASE HELP! best answer gets brainiest!!
ONLY QUESTIONS, 51 to 55
please answer in detail!
Answer:
[tex]x + ( - 43) = 102 \\ x - 43 = 102 \\ x = 102 + 43 \\ x = 145[/tex]
Step-by-step explanation:
Let the unknown number be represented by x
since sum means addition, we are adding the unknown to -43 and equating it to 102 which is said to be the final answer.
After equating, we find out that we have two symbols and + multiplied by - is always -, giving us an equation as in step 2
after collecting like terms , we get an easy linear equation.
im not sure how to do the second question. Does anyone know how to do this?
Answer:
x = 45 Yes
Step-by-step explanation:
x+3x+2x+90= 360°
6x= 270
x=45
A= 2x = 90°
so yes both A and B makes 90° so they should be parallel
u + ka = ba, solve for a
Answer:
[tex]u+ka=ba\\u=ba-ka\\u=(b-k)a\\a=\frac{u}{b-k}[/tex]
please help me with this math problem
[tex]\frac{3}{4} +\frac{1}{6} =\frac{18}{24} +\frac{4}{24} =\frac{22}{24}[/tex]
but 22/24 can be reduced to:
[tex]\frac{22}{24} =\frac{11}{12}[/tex]
a An envelope costs 5 pence and a stamp costs s pence. Write down an expression for the cost of: i a stamped envelope ii 6 stamped envelopes iii n stamped envelopes. b Expand the brackets for your answers to parts ii and iii
help please
(A) stamped envelope will cost 5+s pence
6 stamped envelopes will cost 6(5+s) pence
n stamped envelopes will cost n(5+s) pence
(B) expanded form of the ii part is 30+6s pence
and expanded form of the iii part is 5n+ns pence
As an envelope cost 5 pence and stamp cost s pence
(I) to get an stamped envelope we need to buy an envelope and the we have to get a stamp so the collective sum will be the cost that is
5+s pence
(II)to get 6 stamped envelope we need to buy 6 envelopes and the we have to get 6 stamps so the collective sum will be the cost that is
6(5+s) pence
(III))to get n stamped envelope we need to buy n envelopes and the we have to get n stamps so the collective sum will be the cost that is
n(5+s) pence
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heh I kinda don't have my notes on this problem please look at the picture and help me thank you
Answer:
Step-by-step explanation: 6^4 would be 1296 because its 6 times 6 times 6 times 6. Then 6 times 6 times 6 times 6 times 6 times 6 times 6 times 6 would be 1,679,616. 6 times 6 times 6 would be 216. 1,679,616/216 would be 7776. 1296 times 7776 is 10,077,696.
Hoped This Helped!
Directions: Write a proof for the following.
Given: Isosceles △ABC with legs AB and AC, BD ⊥DC and CE⊥BE
Prove: BD ≅ CE
The two column method can be used to prove that BD is congruent to CE BD ≅ CE as follows;
Statement [tex]{}[/tex] Reasons
1. ΔABC is an isosceles triangle [tex]{}[/tex] 1. Given
2. AB and AC are legs of ΔABC [tex]{}[/tex] 2. Given
3. BD ⊥ DC [tex]{}[/tex] [tex]{}[/tex] [tex]{}[/tex] [tex]{}[/tex] [tex]{}[/tex] 3. Given
CE ⊥ BE
4. ∠BDC = 90° and ∠CEB = 90° [tex]{}[/tex] 4. Definition of perpendicular lines
5. ∠BDC = ∠CEB [tex]{}[/tex] [tex]{}[/tex] [tex]{}[/tex] [tex]{}[/tex] 5. Substitution property
6. ∠BDC ≅ ∠CEB [tex]{}[/tex] [tex]{}[/tex] [tex]{}[/tex] [tex]{}[/tex] 6. Definition of congruency
7. ∠ABC ≅ ∠ACB [tex]{}[/tex] [tex]{}[/tex] [tex]{}[/tex] [tex]{}[/tex] 7. Base angles of an isosceles triangle
8. [tex]\overline{BC}[/tex] ≅ [tex]\overline{BC}[/tex] [tex]{}[/tex] [tex]{}[/tex] [tex]{}[/tex] [tex]{}[/tex] [tex]{}[/tex] 8. Reflexive property of congruency
9. ΔBCE ≅ ΔCBD [tex]{}[/tex] [tex]{}[/tex] [tex]{}[/tex] [tex]{}[/tex] 9. SAA congruency postulate
10. BD ≅CE [tex]{}[/tex] [tex]{}[/tex] [tex]{}[/tex] [tex]{}[/tex] [tex]{}[/tex] [tex]{}[/tex] 10. CPCTC
What are the condition for congruency of two shapes?Two figures are congruent if they have the same size and shape.
The properties, postulates, and theorem used in the prove that BD ≅ CE are as follows;
Perpendicular lines;
Perpendicular lines are lines that form 90° angles where they intersect.
Substitution property
The substitution property of equality states that if one quantity a = b, then b can be substituted for a in equations and expression, such that the value of the expressions and equations remain the same.
Definition of congruency
Congruent figures are figures that have the same shape and size
Base angles of an isosceles triangles
The base angles of an isosceles triangle are congruent
Reflexive property
The reflexive property of congruency states that a figure is congruent to itself
SAA congruency postulate
The Side-Angle-Angle, SAA congruency postulate states that if two angles and the non included side of one triangle are congruent to two angles and the non included side of the other triangle, then the two triangles are congruent.
CPCTC
Corresponding Parts of Congruent Triangles are Congruent, CPCTC states that the corresponding parts of congruent triangles are also congruent.
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SHOW WORK FOR BRAINLIST
Answer:
True, True, False, True
Step-by-step explanation:
For line 2:
[tex]0 + 5(2) = 10[/tex]
[tex]0 + 10 = 10[/tex]
True
-2x - 2y = 4-------> -x - y = 2
x + 5y = 10-----> x + 5y = 10
--------------
4y = 12
y = 3, x = -5
(-5, 3) is a solution to the system----True
(4, 10) is a solution to the system----False
For Line 1:
[tex] - 2( - 10) - 2(8) = 4[/tex]
[tex]20 - 16 = 4[/tex]
True
Describe the end behavior of the graph of the function:
g(x) = 7x7 + 12x5-6x³2x-18
The end behavior of the function is as x → -∞, f(x) → -∞ and s x → +∞, f(x) → +∞.
What is the end behavior of a function?The nature of the value when the function parameter gets closer to +∞ and - ∞ is the end behavior of a function. The term with the highest degree determines how a polynomial function will behave in the end.
Look at the polynomial function's leading term to identify its final behavior. The leading term will dominate the graph because it has the highest power and will therefore grow much more quickly than the other terms as x gets very large or very small.
The given function is f(x) = 7x⁷ + 12x⁵ - 6x³ + 2x - 18
Graph the function. From the graph, the end behavior of the function is given as
As x → -∞, f(x) → -∞
As x → +∞, f(x) → +∞
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A garden table and a bench cot $572 combined. The garden table cot $78 le than the bench. What i the cot of the bench?
The cost of the bench is $325 and the cost of the garden table is $247.
The situation given in the question can be solved by using equation, with two unknown variables, x is the cost of the garden table and y is teh cost of the bench. Considering the garden table is $78 less than the bench. We get the equation for the value of x, then we substitute it in sum equation 1 to get the value of bench.
x+y=$572 ----------------(1)
x=y-$78 ---------------(2)
Substitute equation 2 in 1, we get.
y-$78+y=$572
2y-$78=$572
2y=$572+$78
2y=$650
y=650/2
y=$325
We got the cost of the bench, we substitute this value in equation 2, to get the value of garden table.
x=y-$78
x=$325-$78
x=$247
Hence, the cost of the bench is $325 and garden table is $247.
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Answer Choices:
y=1/3x+11/3
y=-1/3x+11/3
y=11/3x+1/3
y=11/3x-1/3
The linear function graphed is defined as follows:
y = -1/3x + 11/3.
What is a linear function?The slope-intercept representation of a linear function is given as follows:
y = mx + b
The coefficients of the function and their meaning are listed as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x increases by one.b is the y-intercept of the function, which is the value of the function when it's graph crosses the y-axis.From the graph and from the options, the function crosses the y-axis at y = 11/3, hence the intercept is given as follows:
b = 11/3.
When x increases by 5, from 0 to 5, the function decays from 11/3 to 2, hence the slope is obtained as follows:
m = (2 - 11/3)/5 = (6/3 - 11/3) x 1/5 = -5/3 x 1/5 = -1/3.
Hence the equation is:
y = -1/3x + 11/3.
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What’s 6 divide by 3.360
Answer:
1.786
Step-by-step explanation:
Two ships, one sailing at 20mi/h and the other at 35mi/h, left port at the same time. Three hours later they were
110mi apart. If you had to find the angle between their courses an equation that could be used to solve this problem is:
Answer:
Step-by-step explanation:
Bruno has a rectangular wooden deck that measures 4.6 meters by 2.3 meters. Bruno builds an addition to the deck ... Bruno has a rectangular wooden deck that measures 4.6 meters by 2.3 meters. Bruno builds an addition to the deck that makes it 2.5 meters longer. What is the perimeter now.
The perimeter of the rectangular wooden deck, given the measurement of the deck and the addition, can be found to be 18. 8 meters
How to find the perimeter?The perimeter of a rectangular figure can be found by the formula:
= Length + Length + Width + Width
The length was increased by 2. 5 meters and so the new length is:
= 4. 6 + 2. 5
= 7. 1 meters
The new perimeter is therefore:
= 7. 1 + 7. 1 + 2. 3 + 2. 3
= 14. 2 + 4. 6
= 18. 8 meters
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5. Solve the system of equations
7x-4y+8z=37
3x+2y-4z=1 (note: the last equation represents a sphere with centre (0,0,0), radius √14)
x²+y²+z²=14
Answer:
Step-by-step explanation:
as
The y-intercept of the line that is parallel to y=5x-3 that goes through (1,7)
Answer:
y = 5x + 2
Step-by-step explanation:
slope is 5
x = 1
y = 7
Use this to find b for the new equation
y = mx + b
7 = (5)(1) + b
7 = 5 + b Subtract 5 from both sides
2 = b
y = mx + b
y = 5x + 2
the perimeter of a rectangular painting is 370 cm. If the width of the painting is 87 cm, what is it's length?
Answer:
196 cm
Step-by-step explanation:
Perimeter of rectangle=2(L+W)
P=370 cm
W=87 cm
L=?
P=2(L+W)
370 cm=2(L+87 cm)
370 cm=2L+174 cm
379 cm - 174 cm=2L
2L=196
2/2L=196/2
L=98 cm
Are triangles def and lnm similar if ln equals 5, mn equals 3, de equals 10, and fe equals 6? triangles lnm and def with angles n and e marked with the right angle symbol no, the corresponding sides are not proportional no, the corresponding angles are not congruent yes, by the sss similarity postulate yes, by the sas similarity postulate
The given triangles DEF and LNM are similar "by the SSS similarity postulate"
As given in the question, for LNM:
∠N=90°, LN(base)=5 and MN(prependicular)=3
and for DEF:
∠E=90°, DE(base)=10 and MN(prependicular)=6
Two triangles are similar when all their corresponding angles are congruent.
So far we have ∠N≅∠E=90°
Now, for the remaining angles, we first compare ∠L and ∠D.
From Pythagoras' theorem, we get:
For triangle LNM
[tex]LM^{2}=MN^{2}+LN^{2}\\LM=\sqrt{3^{2}+5^{2}}\\LM=\sqrt{34}[/tex]
For triangle DEF
[tex]DF^{2}=EF^{2}+DE^{2}\\DF=\sqrt{6^{2}+10^{2}}\\DF=\sqrt{136}\\DF=2\sqrt{34}[/tex]
Now we have all sides for both triangles and we compare the ratio of corresponding sides;
Side 1: LN:DE = 5:10 = 1:2
Side 2: MN:FE = 3:6 = 1:2
Side 3: LM:DF = [tex]\sqrt{34}[/tex]:[tex]2\sqrt{34}[/tex] = 1:2
As all three ratios are the same, by SSS similarity postulate, we can deduce that triangles LNM and DEF are similar.
This problem can also be solved with the other two (SAS & AA) similarity postulates.
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Answer: Option (C) : Yes, by the SSS Similarity Postulate
Step-by-step explanation:
The model shows the area (in square units) of each part of a rectangle. Use the model to find missing values that complete
the expression.
?
12
?
16
12+16=+D
Explain your reasoning.
Using the given model, we can complete the expression
12 + 16 = 4 × (4 + 3).
What are the area of a rectangle and a square?
The area of a rectangle having length "l" and breadth "b" is
Area of a Rectangle = l × b.
The area of a square with side "a",
Area of a square = side².
Let the given expression be 12 + 16 = x × (y + x)
For the given figure the area of the square which is displayed in pink portion can be expressed as
Area = y²
16 = y²
Taking square root on both sides, we get
y = 4.
Now for the red part, we get the length of the rectangle i.e., y = 4.
Area of a rectangle = length * breadth
12 = 4 * x
x = 3.
Hence, the expression would look like
12 + 16 = 4 × (4 + 3)
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how do I find the perimeter correctly and explain my answer
Answer:
The perimeter of [tex]\triangle[/tex][tex]PQR[/tex] is [tex]16[/tex] feet
Step-by-step explanation:
The perimeter of [tex]\triangle PQR[/tex] can be calculated as follows
Since [tex]\overline{PQ} \cong \overline{PR}[/tex] , then the length of [tex]PQ[/tex] is equal to the length of [tex]PR[/tex]
[tex]PQ = PR = 5~\text{feet}[/tex]
Since the angle [tex]\angle PSR[/tex] is [tex]90^{\circ}[/tex], then [tex]\triangle PSR[/tex] is a right triangle
Since [tex]\triangle PSR[/tex] is a right triangle, then the length of [tex]RS[/tex] can be calculated by the Pythagorean theorem as follows
[tex]c^{2}=a^{2}+b^{2}[/tex]
Where [tex]c[/tex] is the hypotenuse or the side [tex]PR[/tex], [tex]a[/tex] is the side [tex]RS[/tex], and [tex]b[/tex] is the side [tex]PS[/tex]
Substitute [tex]5[/tex] for [tex]PR[/tex], [tex]4[/tex] for [tex]PS[/tex] into the Pythagorean theorem
[tex]5^{2}=a^{2}+4^{2}[/tex]
Simplify the equation
[tex]25=a^{2}+16[/tex]
Move [tex]16[/tex] from the right side to the left side and change its sign to negative
[tex]25-16=a^{2}[/tex]
Simplify the equation
[tex]9 = a^{2}[/tex]
Find the value of [tex]a[/tex] by taking square root of both sides of the equation
[tex]\sqrt{9}=\sqrt{a^{2}}[/tex]
[tex]3 = a[/tex]
As a matter of fact the square root of [tex]9[/tex] are [tex]3[/tex] and [tex]-3[/tex], but disregard the negative value since the length value is never negative
Since the value of [tex]a[/tex] is [tex]3[/tex], then the length of [tex]RS[/tex] is [tex]3[/tex] feet
Since the angle [tex]\angle PSR[/tex] is [tex]90^{\circ}[/tex], then angle [tex]\angle PSQ[/tex] is also [tex]90^{\circ}[/tex] or
[tex]\angle PSQ = \text{straight angle}-90^{\circ}[/tex]
[tex]\angle PSQ = 180^{\circ}-90^{\circ}=90^{\circ}[/tex]
Since [tex]\overline{PQ} \cong \overline{PR}[/tex] and [tex]\angle PSQ = \angle PSR[/tex], then [tex]\triangle PSR \cong \triangle PSQ[/tex]
Since [tex]\triangle PSR \cong \triangle PSQ[/tex], then the length of [tex]RS[/tex] is equal to the length of [tex]QS[/tex]
[tex]RS=QS=3~\text{feet}[/tex]
The perimeter of [tex]\triangle PQR[/tex] is the sum of the length of the following sides
[tex]\text{the perimeter of} ~\triangle PQR= PQ+QS+RS+PR[/tex]
Substitute [tex]5[/tex] for [tex]PQ[/tex], [tex]3[/tex] for [tex]QS[/tex], [tex]3[/tex] for [tex]RS[/tex], [tex]5[/tex] for [tex]PR[/tex] in the expression of the perimeter
[tex]\text{the perimeter of} ~\triangle PQR= 5+3+3+5[/tex]
Simplify the equation
[tex]\text{the perimeter of} ~\triangle PQR=16~\text{feet}[/tex]
Hence the perimeter of [tex]\triangle{PQR}[/tex] is [tex]16~\text{feet}[/tex]
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Practice
1. Consider the functions k(x)=x-1, m(x) = x + 2, n(x) = x - 3, and f(x) = k(x) m(x) - n(x).
a. Graph k(x), m(x), and n(x).
b. Determine the degree of the function f(x). Explain
your reasoning.
c. Determine the zeros of f(x). Explain your reasoning.
d. Determine the intervals over which the value of f(x) is
positive. Determine the intervals over which the value
of f(x) is negative. Explain your reasoning.
e. Sketch f(x).
AY
X
(a) k(x) = x-1, m(x) = x+ 2 , n(x) = x - 3 all shown into the graph .
(b) The degree of the function fn(x) is 3.
(c) The zeros of the function fn(x) is x = 1 , x = -2 and x = 3.
(d) The intervals over which the value of function f(x) is negative (0,6).
What is function explain?
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range.
Given that;
k(x) = x - 1
m(x) = x + 2
n(x) = x - 3
[tex]f(x) = k(x)\times m(x)\times n(x)[/tex]
[tex]f(x) = (x-1)\times (x+2)\times (x-3)[/tex]
[tex]f(x) = (x^2+x-2)(x-3)[/tex]
[tex]f(x) = x^3 +x^2-2x-3x^3-3x+6[/tex]
[tex]f(x) = x^3-2x^2-5x+6[/tex]
a) k(x) = x-1,
m(x) = x+ 2
n(x) = x - 3
all shown into the graph .
b)[tex]f(x) = (x-1)\times (x+2)\times (x+3)[/tex]
[tex]f(x) = x^3-2x^2-5x+6[/tex]
∴degree of function is 3.
degree of function/polynomial is the highest power/degree of the polynomial's monomials.
c) for finding zeros put F(x) = 0 and solve for x
[tex]f(x) = (x-1)\times (x+2)\times (x-3)\\f(0) = (0-1)\times (0+2)\times (0-3)\\[/tex]
x = 1 , x = -2 and x = 3 are the zeros of f(x).
d) for y-intercept put x = 0
f(0) = (0-1)(0+2)(0-3)
f(0)=6
y-intercept is (0,6).
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A statistics student from a large high school takes a random sample of 200 students and finds that 123 are actively
involved in a political party. A 99% confidence interval for the proportion of students at this school who are actively
involved in a political party is (0.526, 0.704). Which statement correctly interprets the interval?
O The statistics student can be 99% confident that 62% of students from this school are actively involved in a
political party.
O There is a 99% probability that the proportion of students at this school who are actively involved in a political
party lies between 0.526 and 0.704.
If this procedure is repeated many, many times, the true proportion of students at this school who are actively
involved in a political party will be captured 99% of the time.
O The statistics student can be 99% confident that the interval from 0.526 to 0.704 captures the true proportion of all
students at this school who are actively involved in a political party.
The last option is correct.
The statistics student can be 99% confident that the interval from 0.526 to 0.704 captures the true proportion of all students at this school who are actively involved in a political party.
What is political party?
A political party is a group that arranges candidates to run in elections in a certain nation. It is typical for party members to share similar political viewpoints, and parties may support particular ideologies or policy objectives.
Given: A statistics student from a large high school takes a random sample of 200 students and finds that 123 are actively involved in a political party.
A 99% confidence interval for the proportion of students at this school who are actively involved in a political party is (0.526, 0.704).
Hence, the statistics student can be 99% confident that the interval from 0.526 to 0.704 captures the true proportion of all students at this school who are actively involved in a political party.
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What are the domain and range of each relation?
Drag the answer into the box to match each relation.
The domain of the first function is {-2,0,2,4} and range is {-3,-1,0} and the domain of second function is {-3,-1,0,3,3} and the range is {-1,0,1,2,3}.
The domain of a function is the set of values that we are allowed to plug into function. This set is the x- values in a function. The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x-value in.
The domain is the x- value of the function and as we can see the mapping on the top left is assigned as x, hence the value of x is {-2,0,2,4} and the range is the y value of the function, as assigned {-3,-1,0}.
In the graph below, the domain is {-3,-1,0,3,3} as it is the x- values and the range is y value of the point given as {-1,0,1,2,3}.
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Ephemeral services corporation (esco) knows that nine other companies besides esco are bidding for a $900,000 government contract. Each company has an equal chance of being awarded the contract. If esco has already spent $100,000 in developing its bidding proposal, what is its expected net profit?.
The expected net profit would be $100,000
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
E(X) = (1/9) × $900,000E(X)=0.111111111×$900,000E(X)= $100,000Therefore the expected net profit would be $100,000Hence,The expected net profit would be $100,000
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I really need help can someone help
The required measure of m∠BVC is 90 degrees in the given figure.
What is Parallelogram?A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.
A parallelogram is a square and a rhombus is a square.
We have been given a figure which shows a rhombus as a parallelogram
The adjacent sides of a parallelogram must be equal, and the angles formed by the four sides must be 90 degrees for a rhombus to be a square.
According to the given figure,
This represents m∠BVC = 90°
Therefore, the required measure of m∠BVC is 90 degrees.
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Volume = 27 ft³
S
8 =
S
feet
S
Answer:
it is 67ft^3
Step-by-step explanation:
5 times 5 times 5 is 67
Machine A makes 144 parts in 6 hours. Machine B makes 468 parts in 9 hours. How many more parts can Machine B make after 12 hours?
Answer:
Step-by-step explanation: Machine A makes 144 parts in 6 hours. Machine B makes 468 parts in 9 hours. If we divide 144 from 6 we will get 24 parts per hour. 468 divided by 9 would be 52. Now 52 times 12 is 624. 24 times 12 is 288 So if we subtracted 624-288=336.
So Machine B Makes 336 more parts after 12 hours. Hoped this helped!
state the y-intercept b, of the linear graph
Answer:
y-intercept b = 2
Step-by-step explanation:
y-intercept is the point where the line intersects the y-axis.so, at y-intercept the x-coordinate is 0.
In this graph the line intersects the y-axis at (0,2).
So, y -intercept b = 2
Simplify
^3✓-8x^24 y^36
[tex]\sqrt[3]{-8x^{24}y^{36}} = \sqrt[3]{-8}\cdot \sqrt[3]{x^{24}}\cdot \sqrt[3]{y^{36}}[/tex]
[tex]\sqrt[3]{8}=-2[/tex] because [tex](-2)(-2)(-2)= -8[/tex]
[tex]\sqrt[3]{x^{24}}=x^8[/tex] because [tex](x^8)(x^8)(x^8)=x^{24}[/tex]
[tex]\sqrt[3]{y^{36}}=y^{12}[/tex] because [tex](y^{12})(y^{12})(y^{12})=y^{36}[/tex]
Therefore [tex]\sqrt[3]{-8x^{24}y^{36}} = -2x^8y^{12}[/tex]
Answer:
[tex]-2x^8y^{12}[/tex]
Step-by-step explanation:
Given expression:
[tex]\sqrt[3]{-8x^{24}y^{36}}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}:[/tex]
[tex]\implies \sqrt[3]{-8}\sqrt[3]{x^{24}}\sqrt[3]{y^{36}}[/tex]
[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]
[tex]\implies \left(-8\right)^{\frac{1}{3}}\left(x^{24}\right)^{\frac{1}{3}}\left(y^{36}\right)^{\frac{1}{3}}[/tex]
Rewrite 8 as 2³:
[tex]\implies \left(-2^3\right)^{\frac{1}{3}}\left(x^{24}\right)^{\frac{1}{3}}\left(y^{36}\right)^{\frac{1}{3}}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies -2^{\frac{3}{3}}x^{\frac{24}{3}}y^{\frac{36}{3}}[/tex]
Simplify:
[tex]\implies -2x^8y^{12}[/tex]
what is 15/16 groups of what size
Step-by-step explanation:
your welcome hope this helps
