Question

By what number should (–15)^–1 be divided so that quotient may be equal to (–15)^–1?

Answer 1

Let (–15)^–1 be divided by x to get quotient (–15)^–1.

So, ${\displaystyle \frac{{(-15)}^{-1}}{x}={(-15)}^{-1}}$

⇒ ${\displaystyle \frac{{(-15)}^{-1}}{{(-15)}^{-1}}=x}$

⇒ x = (–15)^{–1 + 1}  ...[∵ a^m + aⁿ = (a)^{m – n}]

⇒ x = (–15)⁰ = 1  ...[∵ a⁰ = 1]