Question

simplify.
125^{\frac{2}{3}}

Explanation:

Step1: Rewrite 125 as a power of 5

$125 = 5^3$, so $125^{\frac{2}{3}}=(5^3)^{\frac{2}{3}}$

Step2: Apply power - of - a - power rule

According to the rule $(a^m)^n=a^{mn}$, we have $(5^3)^{\frac{2}{3}}=5^{3\times\frac{2}{3}}$

Step3: Calculate the exponent

$3\times\frac{2}{3}=2$, so $5^{3\times\frac{2}{3}} = 5^2$

Step4: Evaluate $5^2$

$5^2=25$

Answer:

25