Question

What expression is equivalent to (^3√2^5)^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}}}\\\\ -------------------------------\\\\ \left( \sqrt[3]{2^5} \right)^{(1)/(4)}\implies \left( 2^{(5)/(3)} \right)^{(1)/(4)}\implies 2^{(5)/(3)\cdot (1)/(4)}\implies 2^{(5)/(12)}`

Answer 2

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