# How do you simplify (6^3)^4 / 12^6?

Jun 9, 2017

${3}^{6}$

Leave it in this form.

#### Explanation:

Raising a power to a power, multiply the indices:

${\left({6}^{3}\right)}^{4} / \left({12}^{6}\right) = {6}^{12} / {12}^{6}$

Write the bases as the product of prime factors:

${6}^{12} / {12}^{6} = {\left(2 \times 3\right)}^{12} / {\left({2}^{2} \times 3\right)}^{6}$

Raising a power to a power, multiply the indices:

$= \frac{{2}^{12} \times {3}^{12}}{{2}^{12} \times {3}^{6}}$

Subtract the indices of like bases:

$= \frac{\cancel{{2}^{12}} \times {3}^{12}}{\cancel{{2}^{12}} \times {3}^{6}} = {3}^{6}$