# How do you simplify and write (2 times 10^4)(4.1 times 10^3) in scientific notation?

Oct 27, 2017

See a solution process below:

#### Explanation:

First, rewrite the expression as:

$\left(2 \times 4.1\right) \left({10}^{4} \times {10}^{3}\right) \implies 8.2 \left({10}^{4} \times {10}^{3}\right)$

Now, use this rule for exponents to complete the simplification:

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

$8.2 \left({10}^{\textcolor{red}{4}} \times {10}^{\textcolor{b l u e}{3}}\right) \implies 8.2 \times {10}^{\textcolor{red}{4} + \textcolor{b l u e}{3}} \implies 8.2 \times {10}^{7}$