Question

WHAT IS THE SIMPLIFIED FORM OF THE EXPRESSION (13)^1/2DIVIDED BY (169)^3/2?

Answer 1

$$\begin{gathered} \frac{{\left(13\right)}^{1/2}}{{\left(169\right)}^{3/2}} \\ =\frac{{\left(13\right)}^{1/2}}{{\left({13}^2\right)}^{3/2}} \\ =\frac{{\left(13\right)}^{1/2}}{{\left(13\right)}^3} \\ ={13}^{\frac{1}{2}-3}\left[\mathrm{as},{\mathrm{a}}^{\mathrm{m}}÷{\mathrm{a}}^{\mathrm{n}}={\mathrm{a}}^{\mathrm{m}-\mathrm{n}}\right] \\ ={13}^{-\frac{5}{2}} \\ ={\left(\frac{1}{13}\right)}^{5/2}\left[\mathrm{as},{\mathrm{a}}^{-\mathrm{m}}=\frac{1}{{\mathrm{a}}^{\mathrm{m}}}\right] \end{gathered}$$