MATH SOLVE

2 months ago

Q:
# Evaluate each expression (25^-3/2)^1/3

Accepted Solution

A:

Answer:[tex]\large\boxed{\left(25^{-\frac{3}{2}}\right)^\frac{1}{3}=\dfrac{1}{5}}[/tex]Step-by-step explanation:[tex]\text{Use}\ (a^n)^m=a^{nm}\\\\\left(25^{-\frac{3}{2}}\right)^\frac{1}{3}=25^{-\frac{3}{2}\cdot\frac{1}{3}}=25^{-\frac{1}{2}}\\\\\text{Use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{1}{25^\frac{1}{2}}\\\\\text{Use}\ a^\frac{1}{n}=\sqrt[n]{a}\to a^\frac{1}{2}=\sqrt[2]{a}=\sqrt{a}\\\\=\dfrac{1}{\sqrt{25}}=\dfrac{1}{5}[/tex]