Question

Evaluate: $\frac{3^{-5}\times {10}^{-5}\times 125}{5^{-7}\times 6^{-5}}$.

Answer 1

$\begin{array}{c}\frac{3^{-5}\times {10}^{-5}\times 125}{5^{-7}\times 6^{-5}}=?\\ \Rightarrow \frac{\left(1\right)\times 5^3\times 6^5\times 5^7}{3^5\times {10}^5}\\ \Rightarrow \frac{5^{10}\times {\left(2\times 3\right)}^5}{3^5\times {\left(2\times 5\right)}^5}=\frac{5^{10}\times 2^5\times {3^5}^{}}{3^5\times 2^5\times 5^5}=\\ 5^{\left(10-5\right)}=5^5=3125Ans.\end{array}$