Question

What is the simplified value of the exponential expression 16^1/14

Answer 1

$16=2^4\\\\16^\frac{1}{14}=(2^4)^\frac{1}{14}=2^{4\cdot\frac{1}{14}}=2^\frac{4}{14}=2^\frac{2}{7}=\sqrt[7]{2^2}=\sqrt[7]4$

$\text{used:}\\\\(a^n)^m=a^{n\cdot m}\\\\\sqrt[n]{a^m}=a^\frac{m}{n}$