# How do you simplify 2^2 \cdot 2^4 \cdot 2^6?

Mar 3, 2018

See a solution process below:

#### Explanation:

Use this rule for exponents to simplify the expression:

${x}^{\textcolor{red}{a}} \times {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} + \textcolor{b l u e}{b}}$

${2}^{\textcolor{red}{2}} \times {2}^{\textcolor{b l u e}{4}} \times {2}^{\textcolor{g r e e n}{6}} \implies {2}^{\textcolor{red}{2} + \textcolor{b l u e}{4} + \textcolor{g r e e n}{6}} \implies {2}^{12}$

${2}^{12}$ in its simplest form is 4096

Mar 3, 2018

${2}^{12}$

#### Explanation:

It's easier to think about the problem by writing it out like this:
$\left(2 \cdot 2\right) \cdot \left(2 \cdot 2 \cdot 2 \cdot 2\right) \cdot \left(2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2\right)$
Count the number of twos,
${2}^{12}$
while it helps to think about it that way, the easiest way to solve it is to just add the exponents.
${2}^{2} \cdot {2}^{4} \cdot {2}^{6}$
$2 + 4 = 6$
$6 + 6 = 12$
${2}^{12}$
I hope this helps :)