Question

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

Answer 1

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