# How to simplify (4times10^2) * (1times10^8) in scientific notation?

May 18, 2018

See a solution process below:

#### Explanation:

First, rewrite the expression as:

$4 \times {10}^{2} \times 1 \times {10}^{8} \implies$

$4 \times 1 \times {10}^{2} \times {10}^{8} \implies$

$4 \times {10}^{2} \times {10}^{8} \implies$

$4 \times \left({10}^{2} \times {10}^{8}\right)$

Next, use this rule for exponents to simplify the 10s terms:

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

$4 \times \left({10}^{\textcolor{red}{2}} \times {10}^{\textcolor{b l u e}{8}}\right) \implies$

$4 \times {10}^{\textcolor{red}{2} + \textcolor{b l u e}{8}} \implies$

$4 \times {10}^{10}$