# How do you simplify (1.032times10^-4)/(8.6times10^-5)?

May 29, 2017

See a solution process below:

#### Explanation:

First, rewrite this expression as:

$\left(\frac{1.032}{8.6}\right) \times \left({10}^{-} \frac{4}{10} ^ - 5\right) \implies 0.12 \times \left({10}^{-} \frac{4}{10} ^ - 5\right)$

Next, use this rule of exponents to simplify the 10s term:

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

$0.12 \times \left({10}^{\textcolor{red}{- 4}} / {10}^{\textcolor{b l u e}{- 5}}\right) \implies 0.12 \times {10}^{\textcolor{red}{- 4} - \textcolor{b l u e}{- 5}} \implies 0.12 \times {10}^{\textcolor{red}{- 4} + \textcolor{b l u e}{5}} \implies$

$0.12 \times {10}^{1}$

If we want this in true scientific notation form we need to move the decimal point one place to the right which means we need to subtract $1$ from the 10s exponent:

$0.12 \times {10}^{1} \implies 1.2 \times {10}^{0}$

If we want this in standard form it is:

$1.2 \times {10}^{0} \implies 1.2 \times 1 \implies 1.2$