Question

Simplify
$\frac{7^{-3}\times {12}^{-3}\times 3^{-4}\times 49}{6^{-4}\times 7^{-1}\times 2^{-4}}$

Answer 1

Let $a=\frac{7^{-3}\times {12}^{-3}\times 3^{-4}\times 49}{6^{-4}\times 7^{-1}\times 2^{-4}}$

$=\frac{7^{-3}\times {(3\times 2^2)}^{-3}\times 3^{-4}\times 7^2}{{(2\times 3)}^{-4}\times 7^{-1}\times 2^{-4}}$

$=\frac{7^{-3}\times 3^{-3}\times 2^{-6}\times 3^{-4}\times 7^2}{2^{-4}\times 3^{-4}\times 7^{-1}\times 2^{-4}}$

$=7^{-3+2+1}\times 3^{-3-4+4}\times 2^{-6+4+4}$ since $\frac{a^m}{a^n}=a^{m-n}$

$=7^0\times 3^{-3}\times 2^2$

$=1\times \frac{1}{3^3}\times 4$ since $(a^{-m}=\frac{1}{a^m})$

$a=\frac{4}{27}$

$\therefore \frac{7^{-3}\times {12}^{-3}\times 3^{-4}\times 49}{6^{-4}\times 7^{-1}\times 2^{-4}}=\frac{4}{27}$