# How do you multiply (2.34 xx 10^-8) (5.7 xx 10^-4)?

Mar 30, 2018

See a solution process below:

#### Explanation:

First, rewrite the expression as:

$\left(2.34 \times 5.7\right) \left({10}^{-} 8 \times {10}^{-} 4\right) \implies$

$13.338 \times \left({10}^{-} 8 \times {10}^{-} 4\right)$

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

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

$13.338 \times \left({10}^{\textcolor{red}{- 8}} \times {10}^{\textcolor{b l u e}{- 4}}\right) \implies$

$13.338 \times {10}^{\textcolor{red}{- 8} + \textcolor{b l u e}{- 4}} \implies$

$13.338 \times {10}^{-} 12$

Now, to put this in scientific notation we need to move the decimal point 1 place to the left so we need to add $\textcolor{red}{1}$ to the exponent of the 10s term:

$1.3338 \times {10}^{- 12 + \textcolor{red}{1}} \implies$

$1.3338 \times {10}^{-} 11$