Question

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

Answer 1

Given $\frac{3^{-5}\times {10}^{-5}\times 125}{5^{-7}\times 6^{-5}}$

$=\frac{125\times 5^7\times 6^5}{3^5\times {10}^5}$

$=\frac{125\times 5\times 5\times 5\times 5\times 5\times 5\times 5\times 6^7}{10\times 10\times 10\times 10\times 10\times 3^5}$

$=\frac{125\times 25\times 6\times 6\times 6\times 6\times 6\times 6\times 6}{2\times 2\times 2\times 2\times 2\times 3\times 3\times 3\times 3\times 3}$

$=125\times 25\times 36$

$=5^3\times 5^2\times 6^2$

$5^5\times 6^2=3125\times 36$

$=112500$