# How do you simplify and write (3.2times10^6) (2.6times10^4) in standard form?

Mar 16, 2018

See a solution process below:

#### Explanation:

First, rewrite the expression as:

$\left(3.2 \times 2.6\right) \left({10}^{6} \times {10}^{4}\right) \implies$

$8.32 \times \left({10}^{6} \times {10}^{4}\right)$

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

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

$8.32 \times \left({10}^{\textcolor{red}{6}} \times {10}^{\textcolor{b l u e}{4}}\right) \implies$

$8.32 \times {10}^{\textcolor{red}{6} + \textcolor{b l u e}{4}} \implies$

$8.32 \times {10}^{10}$

To write this in standard form, because the exponent of 10s term is positive we need to move the decimal point 10 places to the right:

$8.32 \times {10}^{10} \implies$

$83 , 200 , 000 , 000$