Question

Which expression is equivalent to ​

Answer 1

Answer:

$2^{\frac{5}{12}}$

Step-by-step explanation:

• The original expression $\sqrt{2^5} ^{\frac{1}{4}}$ can be transformed into $(2^{\frac{5}{3}})^{\frac{1}{4}}$ : both expressions are equivalent, the root of certain number is equivalent to that number power at a fraction whose denominator is the index of the root. The simpliest example for this statement is $\sqrt{x} =x^{\frac{1}{2}}$ (the squared root of x equals x raised at 1/2).
• Now, the expression$(2^{\frac{5}{3}})^{\frac{1}{4}}$ can be simplified by using the power of a power property, which simply states that if $b\neq 0$ and $((b)^n)^m=b^{n\times{m}}$. In this case, then  $(2^{\frac{5}{3}})^{\frac{1}{4}}=2^{\frac{5}{3}\times{\frac{1}{4}}}=2^{\frac{5}{12}}$, which is the final expression.