Question

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

Answer 1

$\frac{3^{-5}\times {10}^{-5}\times 125}{5^{-7}\times 6^{-5}}=\frac{3^{-5}\times (2\times 5{)}^{-5}\times 5^3}{5^{-7}\times (6{)}^{-5}}=\frac{3^{-5}\times 2^{-5}\times 5^{-5}\times 5^3}{5^{-7}\times 6^{-5}}[\because (ab{)}^m=a^m{b}^m]=\frac{3^{-5}\times 2^{-5}\times 5^{-5+3}}{5^{-7}\times 6^{-5}}=\frac{3^{-5}\times 2^{-5}\times 5^{-2}}{5^{-7}\times 2^{-5}\times 3^{-5}}[\because a^m\times a^n=a^{m+n}]=3^{-5-(-5)}\times 2^{-5-(-5)}\times 5^{-2-(-7)}[\because a^m÷a^n=a^{m-n}]=3^{-5+5}\times 2^{-5+5}\times 5^{-2+7}=3^0\times 2^0\times 5^5[\because a^m÷a^n=a^{m-n}]=1\times 1\times 3125[\because a^0=1]=3125$