Question

How can the number 729 be expressed in an exponential or radical form to yield the result as 243

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{know}\mathrm{that}, \\ 729=3\times 3\times 3\times 3\times 3\times 3=3^6 \\ 243=3\times 3\times 3\times 3\times 3=3^5 \\ \mathrm{now}, \\ {\left(3^6\right)}^{5/6}={\left(3\right)}^{6\times \frac{5}{6}}=3^5=243 \\ \mathrm{so},{\left(729\right)}^{\frac{5}{6}}=243\left[\mathrm{exponential}\mathrm{form}\right] \\ \mathrm{now},243={\left(729\right)}^{5/6}={\left[{\left(729\right)}^5\right]}^{1/6}=\sqrt[6]{729} \\ \mathrm{so},\sqrt[6]{729}=243\left[\mathrm{radical}\mathrm{form}\right] \end{gathered}$$