Question

If $a=(\frac{2}{5}{)}^2÷(\frac{9}{5}{)}^0$, then find the value of $a^{-3}$.

• A. $\frac{125}{12}$
• B. $(\frac{125}{8}{)}^2$
• C. $(\frac{125}{2}{)}^{-6}$
• D. $(\frac{5}{2}{)}^5$

Answer 1

The correct option is B $(\frac{125}{8}{)}^2$

Given, $a=(\frac{2}{5}{)}^2÷(\frac{9}{5}{)}^0$

$\therefore a^{-3}=\left[\right(\frac{2}{5}{)}^2÷(\frac{9}{5}{)}^0{]}^{-3}$

$=\left[\right(\frac{2}{5}{)}^2÷1{]}^{-3}$ ...... $(a^0=1)$

$=\left[\right(\frac{2}{5}{)}^2{]}^{-3}$

$=(\frac{2}{5}{)}^{-6}$

$=(\frac{5}{2}{)}^6$

$=\frac{5}{2}\times \frac{5}{2}\times \frac{5}{2}\times \frac{5}{2}\times \frac{5}{2}\times \frac{5}{2}$

$=\frac{125}{8}\times \frac{125}{8}$

$=(\frac{125}{8}{)}^2$