# How do you write (3.00 * 10 ^-2) * (4.768 * 10 ^6) in scientific notation?

Feb 15, 2017

$14.304 \cdot {10}^{4}$

Or

$1.4304 \cdot {10}^{5}$

#### Explanation:

First, we can rewrite this expression as:

$\left(3.00 \cdot 4.768\right) \cdot \left({10}^{-} 2 \cdot {10}^{6}\right) = 14.304 \left({10}^{-} 2 \cdot {10}^{6}\right)$

We can now use this rule for exponents to multiply the 10s terms:

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

$14.304 \left({10}^{\textcolor{red}{- 2}} \cdot {10}^{\textcolor{b l u e}{6}}\right) = 14.304 \cdot {10}^{\textcolor{red}{- 2} + \textcolor{b l u e}{6}} = 14.304 \cdot {10}^{4}$

Or

$1.4304 \cdot {10}^{5}$