Question

Simplify:

`[(343/27)^(-1/3) [(5/7)^-2 ÷ (3/5)^3]`

Answer 1

Given,

`[(343/27)^(-1/3) [(5/7)^-2 ÷ (3/5)^3]`

We need to simplify the given terms.

Thus, `[(343/27)^(-1/3) [(5/7)^-2 ÷ (3/5)^3]`

⇒ `(7^3/3^3)^(-1/3) [(5/7)^-2 ÷ (3/5)^3]`

⇒ `(7/3)^(3 xx (-1)/3) [(7/5)^2 ÷ (3/5)^3]`  ...[∴ (aⁿ)^m = a^nm]

⇒ `(7/3)^-1 [(7/5)^2 ÷ (3/5)^3]`

⇒ `3/7 [(7/5)^2 ÷ (3/5)^3]`  ...`[∵ (a/b)^-n = (b/a)^n, a/b ÷ c/d = a/b xx d/c]`

⇒ `3/7 [7^2/5^2 xx 5^3/3^3]` 

⇒ `[3/7 xx 7^2/5^2 xx 5^3/3^3]`

= `(7 xx 5)/3^2`

= `35/9`

= `3 8/9`

Hence, the required is `3 8/9`.