# How do you write the answer in scientific notation given (7.2times10^-3)^3?

Mar 29, 2017

See the entire solution process below:

#### Explanation:

First, rewrite this expression as:

${\left(7.2\right)}^{3} \times {\left({10}^{-} 3\right)}^{3}$

Next, expand the term on the left:

$\left(7.2 \times 7.2 \times 7.2\right) \times {\left({10}^{-} 3\right)}^{3} \to$

$\left(7.2 \times 7.2 \times 7.2\right) \times {\left({10}^{-} 3\right)}^{3} \to$

$373.248 \times {\left({10}^{-} 3\right)}^{3}$

Next, use this rule for exponents to expand the 10s term:

${\left({x}^{\textcolor{red}{a}}\right)}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} \times \textcolor{b l u e}{b}}$

$373.248 \times {\left({10}^{\textcolor{red}{- 3}}\right)}^{\textcolor{b l u e}{3}} \to$

$373.248 \times {10}^{\textcolor{red}{- 3} \times \textcolor{b l u e}{3}} \to$

$373.248 \times {10}^{-} 9$

Or, moving the decimal place 2 places to the right:

$3.73248 \times {10}^{-} 7$