Question

Find $\frac{(12{)}^6}{162}$

Answer 1

$\frac{{12}^6}{162}$

splitting into factors, we get

$=\frac{{(2\times 3\times 2)}^6}{2\times 81}$

$=\frac{{\left(2^2\right)}^6\times 3^6}{2^1\times 3^4}$

$=\frac{2^{12}\times 3^6}{2^1\times 3^4}$ using ${\left(a^m\right)}^n=a^{mn}$

$=2^{12-1}\times 3^{6-4}$ using $\frac{a^m}{a^n}=a^{m-n}$

$=2^{11}\times 3^2=18,432$