Question

Please Help ASAP Evaluate (64^1/2)^-2/3

Answer 1

Option A.

Explanation:

The given expression is,

`[(64)^{-(1)/(2)}]^{-(2)/(3)}`

By solving the given expression,

`(64)^{-(1)/(2)}=\frac{1}{(64)^{(1)/(2)}}` [Since
`a^(-1)=(1)/(a)`]

`=(1)/(√(64))`

`=(1)/(8)`

Now the expression will be,

`[(64)^{-(1)/(2)}]^{-(2)/(3)}=((1)/(8))^{-(2)/(3)}`

`=8^{(2)/(3)}`

`={(\sqrt[3]{8})^2}`

= 2²

= 4

Therefore, value of the given expression will be 4.

Option (A) will be the answer.