Question

(-27/8)^(2/3) needs work to be shown

Answer 1

First note that (-27/8)^(2/3) = ( (-27/8)^(1/3) )^2

So let's calculate (-27/8)^(1/3) first.

(-27/8)^(1/3) = -27^(1/3) / 8 ^(1/3)
= -3 / 2
because -3^3 = -27 and 2^3 = 8

Now that means that

( (-27/8)^(1/3) )^2 = ( -3 / 2)^2
= (-3)^2/2^2
= ...

Can you take it from here?

Answer 2

\[(\frac{-27}{8})^{\frac{2}{3}}=\frac{-3^{3^{2/3}}}{2^{3^{2/3}}}=(\frac{-3}{2})^2\]