Question

Which expression is equivalent to ((125^(2))/(125^((4)/(3))))

Answer 1

The answer is D, 25.

Answer 2

25

Explanation:

`\text{The given expression is }\left ( \frac{125^2}{(125)^{(4)/(3)}} \right )\\\\\text{We can write the 125 as }125^3\\\\\text{Thus, the expression becomes}\\\\\left ( \frac{125^2}{(5^3)^{(4)/(3)}} \right )\\\\\text{The denominator can be written as }\\\\\left ( \frac{125^2}{(5)^{3\cdot(4)/(3)}} \right )\\\\=\left ( (5^6)/((5)^(4)) \right )\\\\\text{Using the exponent law }(x^a)/(x^b)=x^(a-b)\\\\(5^(6-4)\\\\=5^2\\\\=25`

Thus, last option is correct.