# How do you simplify (9 times 10^2)(2 times 10^10)?

Jun 22, 2018

$1.8 \times {10}^{13}$

#### Explanation:

Split it:

$9 \times 2 \textcolor{w h i t e}{\text{ddd")=color(white)("ddd")18color(white)("ddd") = color(white)("ddd}} 1.8 \times 10$

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${10}^{2} \times {10}^{10} \textcolor{w h i t e}{\text{ddd") = color(white)("ddd")10^(2+10)color(white)("ddd")=color(white)("ddd}} {10}^{12}$

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Putting it all together

$1.8 \times 10 \times {10}^{12} \textcolor{w h i t e}{\text{d")=color(white)("d}} 1.8 \times {10}^{13}$

Jun 22, 2018

$\left(9 \times {10}^{2}\right) \left(2 \times {10}^{10}\right) = \textcolor{b l u e}{18 \times {10}^{12}} = \textcolor{g r e e n}{1.8 \times {10}^{13}}$

#### Explanation:

$\left(9 \times {10}^{2}\right) \left(2 \times {10}^{10}\right) = 9 \times 2 \times {10}^{2} \times {10}^{10}$

$\textcolor{w h i t e}{\text{XXXXXXXXXXX}} = 18 \times {10}^{12}$

(or in standard scientific notation)
$\textcolor{w h i t e}{\text{XXXXXXXXXXX}} = 1.8 \times {10}^{13}$