Question

What is the simplified value of the exponential expression 64 1/4

Answer 1

$\bf a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \qquad \qquad \sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}}\\\\ -------------------------------\\\\ 64^{\frac{1}{4}}\qquad \boxed{64=2^6}\qquad (2^6)^{\frac{1}{4}}\implies 2^{6\cdot \frac{1}{4}}\implies 2^{\frac{6}{4}}\implies 2^{\frac{3}{2}} \\\\\\ \sqrt[2]{2^3}\implies \sqrt{2^{2+1}}\implies \sqrt{2^2\cdot 2^1}\implies 2\sqrt{2}$