# How do you evaluate \frac { ( 3.00\times 10^ { 6} ) ( 2.0\times 10^ { - 3} ) } { 5.0\times 10^ { - 2} }?

Dec 10, 2016

$120 , 000$ or $1.2 \times {10}^{5}$

#### Explanation:

First, rearrange the terms in the numerator:

$\frac{3.00 \times 2.0 \times {10}^{6} \times {10}^{-} 3}{5.00 \times {10}^{-} 2}$

Using the rule for exponents where $\textcolor{red}{{x}^{a} \times {x}^{b} = {x}^{a + b}}$ we can simplify the numerator to:

$\frac{6.00 \times {10}^{6 - 3}}{5.0 \times {10}^{-} 2}$

$\frac{6.00 \times {10}^{3}}{5.0 \times {10}^{-} 2}$

Now using the rule for exponents where $\textcolor{red}{{x}^{a} / {x}^{b} = {x}^{a - b}}$ we can simplify the fraction to:

$\frac{6.00 \times {10}^{\left(3 - - 2\right)}}{5.0}$

$\frac{6.00 \times {10}^{5}}{5.00}$

Expanding the numerator gives us:

$\frac{600000}{5}$

$120000$

Or in scientific notation form:

$1.2 \times {10}^{5}$

Dec 10, 2016

$1.2 \cdot {10}^{5}$

#### Explanation:

((3.00 * 10^6)(2.0 * 10^-3))/(5.0 * 10^-2

multiply out brackets:

$\frac{6.0 \cdot {10}^{3}}{5.0 \cdot {10}^{-} 2}$

divide 6 by 5:

$\frac{1.2 \cdot {10}^{3}}{10} ^ - 2$

and then the powers of 10:

$1.2 \cdot {10}^{5}$

(reason:) law of indices:
$\left({a}^{m} / {a}^{n} = {a}^{m - n}\right)$

$1.2$ is between 1 and 10, so we do not need to change this or the power of 10.

final answer: $1.2 \cdot {10}^{5}$