Question

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

Answer 1

Given:

Consider the given expression is

`5^{-(5)/(2)}* 5^{(9)/(2)}`

To find:

The simplified form of the given expression.

Solution:

We have,

`5^{-(5)/(2)}* 5^{(9)/(2)}`

Using properties of exponents, we get

`=5^{-(5)/(2)+(9)/(2)}`
`[\because a^ma^n=a^(m+n)]`

`=5^{(-5+9)/(2)}`

`=5^{(4)/(2)}`

`=5^(2)`

`=25`

Therefore, the simplified form of given expression is 25.