Question

How to solve 8 to the power of five thirds

Answer 1

$8^\frac{5}{3}=8^{1\frac{2}{3}}=8^{1+\frac{2}{3}}=8\cdot8^\frac{2}{3}=8\sqrt[3]{8^2}=8\sqrt[3]{64}=8\cdot4=32\\\\Used:\\\\a^n\cdot a^m=a^{n+m}\\\\a^\frac{m}{n}=\sqrt[n]{a^m}\\---------------------------------\\Other\ method\\\\8=2^3\\\\8^\frac{5}{3}=(2^3)^\frac{5}{3}=2^{3\cdot\frac{5}{3}}=2^5=32\\\\Used:\\\\(a^n)^m=a^{n\cdot m}$