Question

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

Answer 1

The answer is D, 25.

Answer 2

Answer:

25

Step-by-step explanation:

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

Thus, last option is correct.