# How do you simplify [(4^2)^3]^2?

May 20, 2017

${4}^{12}$

#### Explanation:

According to the 4th index law

${\left({a}^{x}\right)}^{y}$

${a}^{x \times y}$

(4^2)^3)^2

${\left({4}^{2 \times 3}\right)}^{2}$

${\left({4}^{6}\right)}^{2}$

${4}^{6 \times 2}$

${4}^{12}$

May 20, 2017

${4}^{12}$

#### Explanation:

For reference, the index law used here is
${\left({a}^{x}\right)}^{y} = {a}^{x y}$

So. You just apply that index law step by step until there are no more brackets.
${\left[{\left({4}^{2}\right)}^{3}\right]}^{2}$
$= {\left({4}^{2}\right)}^{3 \times 2}$
$= {\left({4}^{2}\right)}^{6}$
$= {4}^{2 \times 6}$
$= {4}^{12}$

That's the simplified answer, which is what you asked for, but if you wanted the answer without any indices;
${4}^{12} = 16 , 777 , 216$

Hope that helps! :)