Question

By what number should (−20)⁻¹ be divided to obtain (−10)⁻¹?

Answer 1

Let the required number be x.
(−20)^-1 ÷ x = (−10)^-1
⇒ $\frac{1}{\left(-20\right)}\times \frac{1}{x}=\frac{1}{\left(-10\right)}$
⇒ $\frac{1}{\left(-20x\right)}=\frac{1}{\left(-10\right)}$
∴ x = $\frac{\left(-10\right)}{\left(-20\right)}=\frac{1}{2}=2^{-1}$
Hence, the required number is 2^-1.