Which expression is equivalent to (StartFraction 125 squared Over 125 Superscript four-thirds Baseline EndFraction?

Question

asked May 2, 2021 97.3k views

2 Answers

Mreq · Answer 1 · 2021-05-07T22:15:10+0000

Answer:

Explanation:

The given expression is

$(\frac{125^(2) }{125^{(4)/(3) } } )$

To simplify this expression, we have to divide powers, which implies to subtract exponenets, as follows

$(\frac{125^(2) }{125^{(4)/(3) } } )=125^{2-(4)/(3) }=125^{(6-4)/(3) }=125^{(2)/(3) }$

Then, we use the exponent property to transform the obtained power to a root

$125^{(2)/(3) }=\sqrt[3]{125^(2) } =\sqrt[3]{15625} =25$

Therefore, the given expression is equal to 25.