# How do you simplify (9.04times10^6)(5.2times10^-4)?

May 29, 2018

$4.7008 \times {10}^{3}$

#### Explanation:

$9.04 \times 5.2 = 47.008$

${10}^{6} \times {10}^{- 4} = {10}^{6 + - 4} = {10}^{2}$

$\left(9.04 \times {10}^{6}\right) \left(5.2 \times {10}^{- 4}\right) = 47.008 \times {10}^{2}$

$4.7008 \times {10}^{3}$

May 29, 2018

See a solution process below:

#### Explanation:

First, rewrite the expression as:

$9.04 \times {10}^{6} \times 5.2 \times {10}^{-} 4 \implies$

$9.04 \times 5.2 \times {10}^{6} \times {10}^{-} 4 \implies$

$\left(9.04 \times 5.2\right) \times \left({10}^{6} \times {10}^{-} 4\right) \implies$

$47.008 \times \left({10}^{6} \times {10}^{-} 4\right)$

Next, multiply the two 10s terms using this rule for exponents:

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

47.008 xx (10^color(red)(6) xx 10^color(blue)(-4) =>

$47.008 \times {10}^{\textcolor{red}{6} + \textcolor{b l u e}{- 4}} \implies$

$47.008 \times {10}^{\textcolor{red}{6} - \textcolor{b l u e}{4}} \implies$

$47.008 \times {10}^{2}$

To put this expression into scientific notation we must move the decimal point one place to the left so we need to add 1 to the 10s exponent:

$47.008 \times {10}^{2} \implies$

$4.7008 \times {10}^{3}$