Question

What expression is equivalent to (^3√2^5)^1/4

Answer 1

Soo first apply the exponent rule (2^5)^1/3*1/4
1/3*1/4= 1/12
so (2^5)^1/12
then you apply the exponent rule again 2^5*1/2
so 5*1/12= 5/12
So the answer would be 2^5/12

Answer 2

$\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad \sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\ -------------------------------\\\\ \left( \sqrt[3]{2^5} \right)^{\frac{1}{4}}\implies \left( 2^{\frac{5}{3}} \right)^{\frac{1}{4}}\implies 2^{\frac{5}{3}\cdot \frac{1}{4}}\implies 2^{\frac{5}{12}}$