Question

How to solve 8 to the power of negative one third

Answer 1

$8^{-\frac{1}{3}}=\dfrac{1}{8^\frac{1}{3}}=\dfrac{1}{\sqrt[3]8}=\dfrac{1}{2}\\\\Used:\\\\a^{-n}=\dfrac{1}{a^n}\\\\a^\frac{1}{n}=\sqrt[n]{a}\\------------------------\\Other\ method\\\\8=2^3\\\\8^{-\frac{1}{3}}=(2^3)^{-\frac{1}{3}}=2^{3\cdot\left(-\frac{1}{3}\right)}=2^{-1}=\dfrac{1}{2}\\\\Used:\\\\(a^n)^m=a^{n\cdot m}\\\\a^{-n}=\dfrac{1}{a^n}$