Question

Use the properties of exponents to simplify the expression: 2532

Answer 1

Question

Use the properties of exponents to simplify the expression: $25^{\frac{3}{2}}$

Answer:

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

Step-by-step explanation:

Given

$25^{\frac{3}{2}}$

Required

Simplify

$25^{\frac{3}{2}}$

Apply the following law of indices

$a^{\frac{m}{n}} = (a^m)^{\frac{1}{n}}$

So, the expression becomes

$25^{\frac{3}{2}} = (25^3)^{\frac{1}{2}}$

Express $25^3$ as 15625

$25^{\frac{3}{2}} = (15625)^{\frac{1}{2}}$

In indices: $a^{\frac{1}{2}} = \sqrt a$

So, we have:

$25^{\frac{3}{2}} = \sqrt{15625$

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