Question

Find x.

`(- 1/7)^-5 ÷ (- 1/7)^-7 = (-7)^x`

Answer 1

Using law of exponents,

a^m ÷ aⁿ = (a)^{m – n}  ...[∵ a is non-zero integer]

Then, `(- 1/7)^(-5 + 7) = (-7)^x`

⇒ `(- 1/7)^2 = (- 7)^x`

⇒ (–7)^–2 = (–7)^x

On comparing powers of (–7), we get

x = –2