Question

Simplify (8^2/3)^4 on edge

Answer 1

Answer:

$\large\boxed{\left(8^\frac{2}{3}\right)^4=256}$

Step-by-step explanation:

$\text{Use}\\\\(a^n)^m=a^{nm}\\\\a^\frac{1}{n}=\sqrt[n]{a}\\---------------\\\\\left(8^\frac{2}{3}\right)^4=\left(8^{\frac{1}{3}\cdot2}\right)^4=\left[\left(8^\frac{1}{3}\right)^2\right]^4=\left(\sqrt[3]8\right)^{2\cdot4}=2^8=256$