# How do you simplify (3times10^-1)(8times10^-5)?

Apr 29, 2017

See the solution process below:

#### Explanation:

First, rewrite the expression as:

$\left(3 \times 8\right) \left({10}^{-} 1 \times {10}^{-} 5\right) \implies 24 \times \left({10}^{-} 1 \times {10}^{-} 5\right)$

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

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

$24 \times \left({10}^{\textcolor{red}{- 1}} \times {10}^{\textcolor{b l u e}{- 5}}\right) \implies 24 \times {10}^{\textcolor{red}{- 1} + \textcolor{b l u e}{- 5}} \implies 24 \times {10}^{-} 6$

Or, to put the expression into correct scientific notation:

$2.4 \times {10}^{-} 5$