Question

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

Answer 1

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

Explanation:

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