Question

Evaluate:

$\left(i\right)(\frac{5}{3}{)}^2\times (\frac{5}{3}{)}^2$

$\left(ii\right)(\frac{5}{6}{)}^6\times (\frac{5}{6}{)}^{-4}$

$\left(iii\right)(\frac{2}{3}{)}^{-3}\times (\frac{2}{3}{)}^{-2}$

$\left(iv\right)(\frac{9}{8}{)}^{-3}\times (\frac{9}{8}{)}^2$

Answer 1

$\left(i\right)(\frac{5}{3}{)}^2\times (\frac{5}{3}{)}^2=(\frac{5}{3}{)}^{2+2}=(\frac{5}{3}{)}^4$

$=\frac{5}{3}\times \frac{5}{3}\times \frac{5}{3}\times \frac{5}{3}=\frac{625}{81}$

$\left(ii\right)(\frac{5}{6}{)}^6\times (\frac{5}{6}{)}^{-4}=(\frac{5}{6}{)}^{6-4}=(\frac{5}{6}{)}^2$

$=\frac{5}{6}\times \frac{5}{6}=\frac{25}{36}\left(iii\right)(\frac{2}{3}{)}^{-3}\times (\frac{2}{3}{)}^{-2}=(\frac{3}{2}{)}^3\times (\frac{3}{2}{)}^2$

$=(\frac{3}{2}{)}^{3+2}=(\frac{3}{2}{)}^5=\frac{3}{2}\times \frac{3}{2}\times \frac{3}{2}\times \frac{3}{2}\times \frac{3}{2}$

$=\frac{243}{32}$

$\left(iv\right)(\frac{9}{8}{)}^{-3}\times (\frac{9}{8}{)}^2=(\frac{9}{8}{)}^{-3+2}=(\frac{9}{8}{)}^{-1}$

$=\frac{8}{9}$