Question

Simplify the following expression.

Answer 1

Answer:

$\huge{ \boxed{ \sf{ \frac{1}{64} }}}$

Step-by-step explanation:

$\star{ \sf{ \: \: \: {4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } }}$

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

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.

$\mapsto{ \sf{ {4}^{ - \frac{11}{3} - ( - \frac{2}{ 3}) } }}$

$\sf{We \: know \: that : ( - ) \times ( - ) = ( + )}$

$\mapsto{ \sf{ {4}^{ - \frac{11}{3} + \frac{2}{3} } }}$

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.

$\mapsto{ \sf{ {4}^{ \frac{ - 11 + 2}{3} } }}$

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

$\mapsto{ \sf{ {4}^{ \frac{ - 9}{3} } }}$

Divide -9 by 3

$\mapsto{ \sf{ {4}^{ - 3} }}$

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

$\sf{ {a}^{ - m} = \frac{1}{ {a}^{m} } }$

$\mapsto{ \sf{ \frac{1}{ {4}^{3} } }}$

Evaluate the power : 4³

$\mapsto{ \sf{ \frac{1}{64} }}$

Hope I helped!

Best regards!:D

~$\text{TheAnimeGirl}$