Question

Simplify: $\frac{3^5\times {10}^5\times 2^5}{5^7\times 6^5}$

Answer 1

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

$=\frac{3^5\times {(2\times 5)}^5\times 5^2}{5^7\times {(2\times 5)}^5}$ $[$using ${\left(ab\right)}^m=a^m{b}^m]$

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

$=3^{5-5}\times 2^{5-5}\times 5^{5+2-7}$ $[$using $\frac{a^m}{a^n}=a^{m-n}]$

$=3^{\circ }{2}^{\circ }{5}^{\circ }$ $[\because a^{\circ }=1]$

$=1$