Question

Evaluate (3/8)^-2x(3/8)^-7 divided by (8/3)⁹​.

Answer 1

$$\begin{gathered} \frac{{\left({\displaystyle \frac{3}{8}}\right)}^{-2}\times {\left({\displaystyle \frac{3}{8}}\right)}^{-7}}{{\left({\displaystyle \frac{8}{3}}\right)}^9} \\ =\frac{{\displaystyle {\left({\displaystyle \frac{3}{8}}\right)}^{-2-7}}}{{\displaystyle {\left({\displaystyle \frac{3}{8}}\right)}^{-9}}}\left[\mathbf{as}\mathbf{,}\mathbf{}{\mathbf{a}}^{\mathbf{m}}\mathbf{}\mathbf{.}\mathbf{}{\mathbf{a}}^{\mathbf{n}}\mathbf{}\mathbf{=}\mathbf{}{\mathbf{a}}^{\mathbf{m}\mathbf{+}\mathbf{n}}\mathbf{}\mathbf{}\mathbf{}\mathbf{and}\mathbf{}\mathbf{}{\mathbf{a}}^{\mathbf{-}\mathbf{m}}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{1}}{{\mathbf{a}}^{\mathbf{m}}}\right] \\ =\frac{{\displaystyle {\left({\displaystyle \frac{3}{8}}\right)}^{-9}}}{{\displaystyle {\left({\displaystyle \frac{3}{8}}\right)}^{-9}}} \\ =1 \end{gathered}$$