Simplify the following expression.

Answer:

[tex] \huge{ \boxed{ \sf{ \frac{1}{64} }}}[/tex]

Step-by-step explanation:

[tex] \star{ \sf{ \: \: \: {4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } }}[/tex]

[tex] \underline{ \: \text{Remember!}} : [/tex] If [tex] \sf{ {x}^{a} \: and \: {x}^{b} }[/tex] are two algebraic terms , then their quotient is given by [tex] \sf{ {x}^{a} \div {x}^{b} = {x}^{a - b} } [/tex]

i.e To divide two terms with the same base, the power of divide is subtracted from the power of the dividend and the same base is taken.

[tex] \mapsto{ \sf{ {4}^{ - \frac{11}{3} - ( - \frac{2}{ 3}) } }}[/tex]

[tex] \sf{We \: know \: that : ( - ) \times ( - ) = ( + )}[/tex]

[tex] \mapsto{ \sf{ {4}^{ - \frac{11}{3} + \frac{2}{3} } }}[/tex]

Now, Simplify : -11/3 and 2/3

While performing the addition or subtraction of like fraction, you just have to add or subtract the numerator respectively in which the denominator is retained same.

[tex] \mapsto{ \sf{ {4}^{ \frac{ - 11 + 2}{3} } }}[/tex]

[tex] \underline{ \text{Remember!}} : [/tex] The negative and positive integers are always subtracted but posses the sign of the bigger integer

[tex] \mapsto{ \sf{ {4}^{ \frac{ - 9}{3} } }}[/tex]

Divide -9 by 3

[tex] \mapsto{ \sf{ {4}^{ - 3} }}[/tex]

[tex] \underline{ \text{Remember!}} : [/tex] If [tex] \sf{ {a}^{ - m}} [/tex] is an algebraic term , where m is a negative integer , then

[tex] \sf{ {a}^{ - m} = \frac{1}{ {a}^{m} } }[/tex]

[tex] \mapsto{ \sf{ \frac{1}{ {4}^{3} } }}[/tex]

Evaluate the power : 4³

[tex] \mapsto{ \sf{ \frac{1}{64} }}[/tex]

Hope I helped!

Best regards!:D

~[tex] \text{TheAnimeGirl}[/tex]

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