Question

Calculate:

`(49^((-3)/2)xx7^-2)/(343^((-4)/3))`

Answer 1

Given,

`(49^((-3)/2)xx7^-2)/(343^((-4)/3))`

We need to simplify the given terms.

Thus, `(49^((-3)/2)xx7^-2)/(343^((-4)/3)) = ((7^2)^((-3)/2) xx 7^-2)/((7^3)^((-4)/3)`

= `(7^(2 xx (-3)/2) xx 7^-2)/(7^(3 xx (-4)/3)`   ...[∴ (a^m)ⁿ = a^mn]

= `(7^-3 xx 7^-2)/7^-4`

= `(7)^(-3 - 2)/(7)^-4`  ...[∴ aⁿ × a^m = a^{n + m}]

= `(7)^-5/(7)^-4`

= `(7)^(-5 - (-4))`  ...`[∴ a^n/a^m = a^(n - m)]`

= `(7)^(-5 + 4)`  ...`[∴ a^-n = 1/a^n]`

= `7^-1`

= `1/7`

Hence, the required is `1/7`.