Question

(64)^-1/2 -(-32)^-4/5

Answer 1

Please see the attachment

Answer 2

$\displaystyle \sf{ {(64)}^{ - \frac{1}{2} } - {( - 32)}^{ - \frac{4}{5} } }$

Given : $\displaystyle \sf{ {(64)}^{ - \frac{1}{2} } - {( - 32)}^{ - \frac{4}{5} } } = \frac{1}{16}$

To find : To simplify the expression

Solution :

Here the given expression is

$\displaystyle \sf{ {(64)}^{ - \frac{1}{2} } - {( - 32)}^{ - \frac{4}{5} } }$

We simplify it as below

$\displaystyle \sf{ {(64)}^{ - \frac{1}{2} } - {( - 32)}^{ - \frac{4}{5} } }$

$\displaystyle \sf{ = {( {8}^{2} )}^{ - \frac{1}{2} } - {{ \{( -2) }^{5} \} }^{ - \frac{4}{5} } }$

$\displaystyle \sf{ = {( 8 )}^{ - \frac{1}{2} \times 2 } - {( - 2)}^{ - \frac{4}{5} \times 5} }$

$\displaystyle \sf{ = {( 8 )}^{ - 1 } - {( - 2)}^{ - 4} }$

$\displaystyle \sf{ = \frac{1}{8} - \frac{1}{ {2}^{4} } }$

$\displaystyle \sf{ = \frac{1}{8} - \frac{1}{ 16 } }$

$\displaystyle \sf{ = \frac{2 - 1}{ 16 } }$

$\displaystyle \sf{ = \frac{ 1}{ 16 } }$

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