# How do you simplify (5 times 10^7)(9 times 10^-3) / (3 times 10^-2) in scientific notation?

Nov 20, 2015

$15 \cdot {10}^{6}$

#### Explanation:

First of all, since the multiplication is commutative, you can deal with numbers and powers of ten separately:

5 times 10^7 \frac{9 times 10^{-3}}{3 times 10^{-2}} = 5* 9/3 times 10^7 \frac{10^{-3}}{10^{-2}

Of course, $5 \cdot \frac{9}{3} = 5 \cdot 3 = 15$.

As for the powers of ten, remember that

${a}^{b} \cdot {a}^{c} = {a}^{b + c}$, and ${a}^{b} / {a}^{c} = {a}^{b - c}$

This means that

${10}^{7} \setminus \frac{{10}^{- 3}}{{10}^{- 2}} = {10}^{7 - 3 - \left(- 2\right)} = {10}^{7 - 3 + 2} = {10}^{6}$