Question

Simplify: ${\left(\frac{5}{8}\right)}^{-3}\times {\left(\frac{4}{5}\right)}^{-3}÷{\left(\frac{4}{5}\right)}^3$

• A. $\frac{5^3}{2^3}$
• B. $\frac{5^4}{2^5}$
• C. $\frac{5^3}{2^4}$
• D. $\frac{5^3}{2^{-3}}$

Answer 1

Answer: (A)

$\frac{5^3}{2^3}$

${\left(\frac{5}{8}\right)}^{-3}\times {\left(\frac{4}{5}\right)}^{-3}÷{\left(\frac{4}{5}\right)}^3$

$={\left(\frac{5}{2^3}\right)}^{-3}\times {\left(\frac{2^2}{5}\right)}^{-3}÷{\left(\frac{2^2}{5}\right)}^3$

$=\frac{5^{-3}}{2^{-9}}\times \frac{2^{-6}}{5^{-3}}÷\frac{2^6}{5^3}$
$=2^{-6-(-9)}\times \frac{5^3}{2^6}$
$=2^{3-6}\times 5^3$
$=2^{-3}\times 5^3$
$=\frac{5^3}{2^3}$

Hence, option $A$ is correct.