Question

Calculate:

`25^((-1)/2) xx 125^(2/3) ÷ 625`

Answer 1

Given,

`25^((-1)/2) xx 125^(2/3) ÷ 625`

We need to simplify the given terms.

Thus, `25^((-1)/2) xx 125^(2/3) ÷ 625`

⇒ `(5^2)^((-1)/2) xx (5^3)^(2/3) ÷ 5^4`

⇒ `(5)^(2 xx (-1)/2) xx (5)^(3 xx 2/3) ÷ 5^4`  ...[∴ (aⁿ)^m = a^nm]

⇒ `(5)^-1 xx (5)^2 ÷ 5^4`

⇒ `(5)^(-1 + 2) ÷ 5^4`   ...[∴ aⁿ × a^m = a^{n + m}]

⇒ `(5)^1 ÷ 5^4`

⇒ `5^(1 - 4)`   ...[∴ aⁿ ÷ a^m = a^{n – m}]

= `5^-3`  ...`[∴ a^-n = 1/a^n]`

= `1/5^3`

= `1/125` 

Hence, the required is `1/125`.