Question

by what number should (4)^-2 be multiplied so that the product is equal to (10)^-2 ?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{required}\mathrm{number}=\mathrm{x} \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{question}: \\ {4}^{-2}\times \mathrm{x}={10}^{-2} \\ \Rightarrow \frac{1}{4^2}\times \mathrm{x}=\frac{1}{{10}^2} \\ \Rightarrow \frac{1}{16}\times \mathrm{x}=\frac{1}{100} \\ \Rightarrow \frac{1}{16}\times \mathrm{x}=\frac{1}{100} \\ \Rightarrow \mathrm{x}=\frac{16}{100}=\frac{4}{25} \\ \mathrm{So},\mathrm{the}\mathrm{required}\mathrm{number}=\frac{4}{25} \end{gathered}$$