Question

Express each of the following rational numbers in power notation:
(i) $\frac{49}{64}$
(ii) $-\frac{64}{125}$
(iii) $-\frac{1}{216}$

Answer 1

We have
(i) $\frac{49}{64}=\frac{7}{8}\times \frac{7}{8}=\frac{(7{)}^2}{(8{)}^2}={\left(\frac{7}{8}\right)}^2$
(ii) $-\frac{64}{125}=-\frac{4}{5}\times -\frac{4}{5}\times -\frac{4}{5}=-\frac{(4{)}^3}{(5{)}^3}={\left(-\frac{4}{5}\right)}^3$
(iii) $-\frac{1}{216}=\frac{-1}{6}\times \frac{-1}{6}\times \frac{-1}{6}=\frac{(-1{)}^3}{(6{)}^3}={\left(\frac{-1}{6}\right)}^3$