Question

Simplify: $\frac{3^5\times {10}^5\times 25}{5^7\times 6^5}$.

Answer 1

$\frac{3^5\times {10}^5\times 25}{5^7\times 6^5}=\frac{3^5\times {\left(2\times 5\right)}^5\times 5^2}{5^7\times {\left(2\times 3\right)}^5}$
$=\frac{3^5\times 2^5\times 5^5\times 5^2}{5^7\times 2^5\times 3^5}$
$$\begin{gathered} =\frac{3^5\times 2^5\times 5^7}{3^5\times 2^5\times 5^7} \\ =3^{5-5}\times 2^{5-5}\times 5^{7-7} \\ =3^0\times 2^0\times 5^0 \\ =1\times 1\times 1=1 \end{gathered}$$