# How do you simplify (10^4)(10^9)?

Feb 5, 2016

$\left({10}^{4}\right) \left({10}^{9}\right) = {10}^{13}$

#### Explanation:

One way is to remember the general relation:
$\textcolor{w h i t e}{\text{XXX}} {b}^{p} \times {b}^{q} = {b}^{p + q}$

Or
$\textcolor{w h i t e}{\text{XXX}} {10}^{4}$ means $10$ multiplied together $4$ times
$\textcolor{w h i t e}{\text{XXX}}$and
$\textcolor{w h i t e}{\text{XXX}} {10}^{9}$ means $10$ multiplied together $9$ times

$\textcolor{w h i t e}{\text{XXX}}$So ${10}^{4} \times {10}^{9}$ will be $10$ multiplied together $13$ times
$\textcolor{w h i t e}{\text{XXX}}$which can be written ${10}^{13}$

Feb 5, 2016

$\left({10}^{4}\right) \left({10}^{9}\right) = {10}^{13}$

#### Explanation:

If $k$ is a positive integer then:

${10}^{k} = \stackrel{\text{k times}}{\overbrace{10 \times 10 \times \ldots \times 10}}$

So if $a$ and $b$ are positive integers then we find:

${10}^{a} \times {10}^{b} = \stackrel{\text{a times" overbrace(10xx10xx...xx10) xx stackrel "b times}}{\overbrace{10 \times 10 \times \ldots \times 10}}$

$= \stackrel{\text{a + b times}}{\overbrace{10 \times 10 \times \ldots \times 10}} = {10}^{a + b}$

In our example, $a = 4$ and $b = 9$ and we find:

$\left({10}^{4}\right) \left({10}^{9}\right) = {10}^{4 + 9} = {10}^{13}$