Question

simplify.
(-8)^{\frac{2}{3}}

Explanation:

Step1: Rewrite the base

We can rewrite -8 as $(-2)^3$. So, $(-8)^{\frac{2}{3}}=((-2)^3)^{\frac{2}{3}}$.

Step2: Apply power - of - a - power rule

According to the power - of - a - power rule $(a^m)^n=a^{mn}$. Here, $m = 3$ and $n=\frac{2}{3}$, so $((-2)^3)^{\frac{2}{3}}=(-2)^{3\times\frac{2}{3}}$.

Step3: Calculate the exponent

$3\times\frac{2}{3}=2$. Then $(-2)^2$.

Step4: Evaluate the result

$(-2)^2 = 4$.

Answer:

4