# How do you simplify (12b^2)^2?

Mar 22, 2018

color(blue)((12b^2)^2=144b^4

#### Explanation:

Given:

We need to simplify ${\left(12 {b}^{2}\right)}^{2}$.

Formula used:

color(blue)((a^m)^n = a^(mn)

We will rewrite the given expression color(red)((12b^2)^2=144b^4 as

$\textcolor{b l u e}{\left({12}^{2}\right) \cdot {\left({b}^{2}\right)}^{2}}$

The first part ${12}^{2}$ can be simplified as follows:

${12}^{2} = 12 \cdot 12 = 144 \text{ }$ Intermediate Result 1

The second part ${\left({b}^{2}\right)}^{2}$ can be simplified using the formula:

color(blue)((a^m)^n = a^(mn)

${\left({b}^{2}\right)}^{2} = {b}^{\left(2 \cdot 2\right)} = {b}^{4} \text{ }$ Intermediate Result 2

We can now use both the Intermediate Result 1 and Intermediate Result 2 to write our final answer.

color(blue)((12b^2)^2=144b^4.

Hope it helps.

Mar 22, 2018

$\therefore = 144 {b}^{4}$
${\left(12 {b}^{2}\right)}^{2}$
$\therefore = \left(12 {b}^{2}\right) \left(12 {b}^{2}\right)$
$\therefore = 144 {b}^{4}$