Question

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

Answer 1

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

$=\frac{3^5\times {10}^5\times 5^2}{5^7\times (2\times 3{)}^5}$

$=\frac{3^5\times {10}^5\times 5^2}{5^7\times 2^5\times 3^5}$ [Since, $(a\times b{)}^m=a^m\times b^m$]

$=\frac{{10}^5\times 5^{2-7}}{(2{)}^5}$ [Since, $\frac{a^m}{a^n}=a^{m-n},a\ne 0$]

$=\frac{(2\times 5{)}^5\times 5^{-5}}{(2{)}^5}$

$=\frac{2^5\times 5^5}{2^5\times 5^5}$ [Since, $(a\times b{)}^m=a^m\times b^m,a^{-m}=\frac{1}{a^m},a\ne 0$]

$=1$

$\therefore \frac{3^5\times {10}^5\times 25}{5^7\times 6^5}=1$