Question

Which expression is equivalent to (StartFraction 125 squared Over 125 Superscript four-thirds Baseline EndFraction? StartFraction 1 Over 25 EndFraction One-tenth 10 25

Answer 1

Answer:

$\frac{125^2}{125^\frac{4}{3}} = 25$

Step-by-step explanation:

Given

$\frac{125^2}{125^\frac{4}{3}}$

Required

Find an equivalent expression

$\frac{125^2}{125^\frac{4}{3}}$

Apply the following law of indices;

$\frac{a^m}{a^n} a^{m-n}$

The expression becomes

$125^{2-\frac{4}{3}}$

Solve the exponents

$125^{\frac{6-4}{3}}$

$125^{\frac{2}{3}}$

Express 125 as 5³

$5^{3^*\frac{2}{3}}$

Solve the exponents

$5^2$

$25$

Hence;

$\frac{125^2}{125^\frac{4}{3}} = 25$