Question

Which expression is the simplest form of (27x^-9)^1/3?

Answer 1

$\sqrt[n]{a^m}=a^\frac{m}{n}\\\\\sqrt[n]{a}=a^\frac{1}{n}\\\\(a^n)^m=a^{nm}\\\\(a\cdot b)^n=a^n\cdot b^n\\\\(27x^{-9})^\frac{1}{3}=27^\frac{1}{3}(x^{-9})^\frac{1}{3}=\sqrt[3]{27}\cdot x^{-9\cdot\frac{1}{3}}=3x^{-3}=\dfrac{3}{x^3}$