Question

If $\frac{2^{10}}{5}\times \frac{2^2}{5}÷{\left(\frac{5}{2}\right)}^{-12}=\frac{5^a}{2}$.Find $a$

Answer 1

$\frac{2^{10}}{5}\times \frac{2^2}{5}÷{\left(\frac{5}{2}\right)}^{-12}=\frac{5^a}{2}$

$\Rightarrow \frac{2^{10}}{5}\times \frac{2^2}{5}\times {\left(\frac{2}{5}\right)}^{-12}=\frac{5^a}{2}$

$\Rightarrow \frac{2^{10}}{5}\times \frac{2^2}{5}\times {\left(\frac{5}{2}\right)}^{12}=\frac{5^a}{2}$

$\Rightarrow \frac{2^{12}}{5^2}\times \frac{5^{12}}{2^{12}}=\frac{5^a}{2}$

$\Rightarrow \frac{5^{10}}{2}=\frac{5^a}{2}$

On comparing both sides, we have

$a=10$

Hence, the correct answer is 10.