Question

Simplify: $\frac{8^{-1}\times 5^3}{4^{-4}\times 625}$

• A. $5$
• B. $\frac{32}{5}$
• C. $\frac{1}{4}$
• D. $4$

Answer 1

The correct option is B $\frac{32}{5}$

$\frac{8^{-1}\times 5^3}{4^{-4}\times 625}$

$=\frac{\left(\frac{1}{8}\right)\times 5^3}{{\left(\frac{1}{4}\right)}^4\times 625}(\because a^{-1}=\frac{1}{a})$

$\Rightarrow =\frac{4^4\times 125}{8\times 625}(\because 5^3=125)$

$\Rightarrow =\frac{256}{8\times 5}$

$\Rightarrow =\frac{32}{5}$

Hence, the correct answer is $\frac{32}{5}$.