Which expression is equivalent to

Question

asked Oct 1, 2021 176k views

1 Answer

Bossi · Answer 1 · 2021-10-06T07:15:35+0000

Answer:

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

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.