Question

Use the law of exponents and simplify:
$\frac{{\left(12\right)}^6}{162}$

Answer 1

Consider, $\frac{(12{)}^6}{162}$

$=\frac{(3\times 4{)}^6}{2\times 9\times 9}$

$=\frac{3^6\times 4^6}{2\times 3^2\times 3^2}$ ... [Using product rule of exponents]

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

$=(3{)}^{6-4}\times (2{)}^{12-1}$ ........ [Using quotient rule]

$=3^2\times 2^{11}$

$=18432$

Hence, the answer is $18432$.