# How do you calculate  (4 times 10 ^-3 )/(8 times 10^-7)?

Feb 28, 2017

$5.0 \times {10}^{3}$

#### Explanation:

$\frac{\textcolor{b l u e}{4 \times {10}^{- 3}}}{\textcolor{red}{8 \times {10}^{- 7}}} \text{ "=" } \textcolor{b l u e}{\frac{4 \times \textcolor{red}{{10}^{7}}}{\textcolor{red}{8} \times {10}^{3}}}$

$= \frac{4}{8} \times {10}^{4}$

$= 0.5 \times {10}^{4}$

As the question's format is of a particular style we should write our answer in the same format (scientific notation).

But written in scientific notation we need 5.0 and not 0.5

so we write $0.5$ as $\text{ } 5.0 \times \frac{1}{10}$

Putting it all together we have:

$5.0 \times \frac{1}{10} \times {10}^{4}$

$5.0 \times {10}^{3}$

Feb 28, 2017

See the entire solution process below:

#### Explanation:

First, rewrite this expression as:

$\left(\frac{4}{8}\right) \left({10}^{-} \frac{3}{10} ^ - 7\right) = 0.5 \times \left({10}^{-} \frac{3}{10} ^ - 7\right)$

Now, use this rule of exponents to simplify the 10s terms:

${x}^{\textcolor{red}{a}} / {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} - \textcolor{b l u e}{b}}$

$0.5 \times \left({10}^{\textcolor{red}{- 3}} / {10}^{\textcolor{b l u e}{- 7}}\right) = 0.5 \times {x}^{\textcolor{red}{- 3} - \textcolor{b l u e}{- 7}} = 0.5 \times {10}^{\textcolor{red}{- 3} + \textcolor{b l u e}{7}} =$

$0.5 \times {10}^{4}$

Or

$5.0 \times {10}^{3}$

Or

$5 , 000$