Question

What expression is equivalent to (x^4/3x^2/3)^1/3?

Answer 1

Answer:

$\large\boxed{x^\frac{4}{3}}$

Step-by-step explanation:

$\left(x^\frac{4}{3}x^\frac{2}{3}\right)^\frac{1}{3}\qquad\text{use}\ a^na^m=a^{n+m}\\\\=\left(x^{\frac{4}{3}+\frac{2}{3}}\right)^\frac{1}{3}=\left(x^\frac{6}{3}\right)^\frac{1}{3}=(x^2)^\frac{1}{3}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=x^{(2)\left(\frac{2}{3}\right)}=x^{\frac{4}{3}}$