Question

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

Answer 1

Answer:

Option A.

Step-by-step explanation:

The given expression is,

$[(64)^{-\frac{1}{2}}]^{-\frac{2}{3}}$

By solving the given expression,

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

           $=\frac{1}{\sqrt{64}}$

           $=\frac{1}{8}$

Now the expression will be,

$[(64)^{-\frac{1}{2}}]^{-\frac{2}{3}}=(\frac{1}{8})^{-\frac{2}{3}}$

                 $=8^{\frac{2}{3}}$

                 $={(\sqrt[3]{8})^2}$

                 = 2²

                 = 4

Therefore, value of the given expression will be 4.

Option (A) will be the answer.