Simplifying numerical expression

Question

I am needing to simplify the following numerical expression:

8 -2/3

Here are my options:

-4, 4, -1/4, 1/4

I have tried everything and I'm not coming up with any of these. Please help.

Answer 1

8^(-2/3) =2^(3*(-2/3)) =2^(-2) =1/2^2 =1/4

Answer 2

Use the hints below :

• $8=2^3$
• $(a^q)^{\frac pq}=a^p$
• $a^{-n}=\dfrac 1{a^n}$

Answer 3

Either there's a typo in the book, or you haven't transcribed it correctly.

Based on the choices, the intended expression was probably $$8^{\left(-\frac{2}{3}\right)}$$ in which case, the simplification works out as \begin{align*} 8^{\left(-\frac{2}{3}\right)} &=\frac {1} {8^ {\left(\frac{2}{3}\right)}} \\[4pt] &=\frac {1} {\Bigl(8^ {\left(\frac{1}{3}\right)}\Bigr)^2} \\[4pt] &=\frac {1} {2^2} \\[4pt] &=\frac {1} {4} \\[4pt] \end{align*}