# How do you multiply (3 x 10^7)(5 x 10^4)?

Mar 7, 2018

See a solution process below:

#### Explanation:

First, rewrite the expression as:

$3 \times {10}^{7} \times 5 \times {10}^{4} \implies$

$3 \times 5 \times {10}^{7} \times {10}^{4} \implies$

$15 \times {10}^{7} \times {10}^{4}$

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

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

$15 \times {10}^{\textcolor{red}{7}} \times {10}^{\textcolor{b l u e}{4}} \implies$

$15 \times {10}^{\textcolor{red}{7} + \textcolor{b l u e}{4}} \implies$

$15 \times {10}^{11}$

If it is necessary to write the solution in correct scientific notation we need to move the decimal point 1 place to the left so we need to add 1 to the 10s exponent:

$15 \times {10}^{11} \implies$

$1.5 \times {10}^{12}$