Question

Simplify:

`(5^(1/2) xx 5^(7/2))/25^(3/2)`

Answer 1

Given,

`(5^(1/2) xx 5^(7/2))/25^(3/2)`

We have to simplify the given expression.

In the given expression, we can write it as `5^(1/2) xx 5^(7/2) ÷ 25^(3/2)`.

⇒ `5^(1/2) xx 5^(7/2) ÷ (5^2)^(3/2)`

⇒ `5^(1/2) xx 5^(7/2) ÷ (5)^3`  ...[∴ xⁿ × x^m = x^{n + m}]

⇒ `5^(1/2 + 7/2) ÷ 5^3`

⇒ `5^(8/2) ÷ 5^3`

⇒ 5⁴ ÷ 5³  ...[∴ xⁿ ÷ x^m = x^{n – m}]

⇒ 5^{4 – 3} = 5¹ = 5

Hence, `(5^(1/2) xx 5^(7/2))/25^(3/2) = 5`.