Question

By multiplying `(5/3)^4` by ______ we get 5⁴.

Answer 1

By multiplying `(5/3)^4` by 81 we get 5⁴.

Explanation:

Let x be multiplied with `(5/3)^4` to get 5⁴.

So, `(5/3)^4 xx x = 5^4`

∴ `x = 5^4/(5/3)^4 = 5^4 xx 3^4 xx 5^-4`

= (5)^{4 – 4} × 3⁴  ...`[∵ a^-m = 1/a^m, a^m xx a^n = (a)^(m + n)]`

= 5⁰ × 3⁴

= 1 × 81

= 81