# How do you simplify (3.8 * 10 ^-5) ( 2.8 * 10 ^-5) in scientific notation?

Apr 11, 2018

See a solution process below:

#### Explanation:

First, rewrite this expression as:

$3.8 \cdot {10}^{-} 5 \cdot 2.8 \cdot {10}^{-} 5 \implies$

$3.8 \cdot 2.8 \cdot {10}^{-} 5 \cdot {10}^{-} 5 \implies$

$10.64 \cdot {10}^{-} 5 \cdot {10}^{-} 5$

Next, we can use this rule of exponents to multiply the 10s terms:

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

$10.64 \cdot {10}^{\textcolor{red}{- 5}} \cdot {10}^{\textcolor{b l u e}{- 5}} \implies$

$10.64 \cdot {10}^{\textcolor{red}{- 5} + \left(\textcolor{b l u e}{- 5}\right)} \implies$

$10.64 \cdot {10}^{\textcolor{red}{- 5} - \textcolor{b l u e}{5}} \implies$

$10.64 \cdot {10}^{-} 10$

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

$10.64 \cdot {10}^{-} 10 \implies$

$1.064 \cdot {10}^{- 10 + 1} \implies$

$1.064 \cdot {10}^{-} 9$