Question

Simplify the expression

Answer 1

`(2.5a^(8n))^3 . (0.4^(7n))^3 = 15.625 * a^(24n) * (0.4^(21))^n`

Solution:

We have to simplify the given expression

Given expression is:

`(2.5a^(8n))^3 . (0.4^(7n))^3`

Use the law of exponent

`(a^m)^n = a^(mn)`

Thus the given expression becomes,

`(2.5a^(8n))^3 . (0.4^(7n))^3 = (2.5)^3(a)^(8n * 3) * (0.4)^(7n * 3)`

Simplify the exponents

`(2.5a^(8n))^3 . (0.4^(7n))^3 = 15.625 * a^(24n) * 0.4^(21n)`

Again use the law of exponent for
`0.4^(21n)`

`0.4^(21n) = (0.4^(21))^n`

Substitute in above expression

`(2.5a^(8n))^3 . (0.4^(7n))^3 = 15.625 * a^(24n) * (0.4^(21))^n`

Thus the given expression is simplified