Question

Explain the difference between the following two expressions.
(-1)^2/4 and (-1)^1/2

Answer 1

`\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^( n)} \qquad \qquad \sqrt[{ m}]{a^( n)}\implies a^{\frac{{ n}}{{ m}}}\\\\ -------------------------------\\\\ (-1)^{(2)/(4)}\implies \sqrt[4]{(-1)^2}\implies \sqrt[4]{(-1)(-1)}\implies \sqrt[4]{1}\qquad \boxed{1^4=1} \\\\\\ \sqrt[4]{1^4}\implies 1\\\\ -------------------------------\\\\ (-1)^{(1)/(2)}\implies \sqrt[2]{(-1)^1}\implies √(-1)\implies i`