Question

Simplify the following expression 5-⁵/2 x 5⁹/2

Answer 1

Given:

Consider the given expression is

$5^{-\frac{5}{2}}\times 5^{\frac{9}{2}}$

To find:

The simplified form of the given expression.

Solution:

We have,

$5^{-\frac{5}{2}}\times 5^{\frac{9}{2}}$

Using properties of exponents, we get

$=5^{-\frac{5}{2}+\frac{9}{2}}$           $[\because a^ma^n=a^{m+n}]$

$=5^{\frac{-5+9}{2}}$

$=5^{\frac{4}{2}}$

$=5^{2}$

$=25$

Therefore, the simplified form of given expression is 25.