Question

Express the following as powers of rational numbers;

729/216 and 144/625

Answer 1

$$\begin{gathered} \frac{729}{216}=\frac{3^6}{6^3}=\frac{3^6}{2^3*3^3}=\frac{3^{6-3}}{2^3}=\frac{3^3}{2^3}={\left(\frac{3}{2}\right)}^3; \\ \frac{144}{625}=\frac{{12}^2}{5^4}=\frac{{12}^2}{{25}^2}={\left(\frac{12}{25}\right)}^2 \end{gathered}$$