Question

Which expression is equivalent to ​

Answer 1

`2^{(5)/(12)}`

Explanation:

• The original expression
  `√(2^5) ^{(1)/(4)}` can be transformed into
  `(2^{(5)/(3)})^{(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
  `√(x) =x^{(1)/(2)}` (the squared root of x equals x raised at 1/2).
• Now, the expression
  `(2^{(5)/(3)})^{(1)/(4)}` can be simplified by using the power of a power property, which simply states that if
  `b\\eq 0` and
  `((b)^n)^m=b^{n*{m}}`. In this case, then
  `(2^{(5)/(3)})^{(1)/(4)}=2^{(5)/(3)*{(1)/(4)}}=2^{(5)/(12)}`, which is the final expression.