# How do you write the answer in scientific notation given (4.5times10^4)^2?

May 18, 2017

See a solution process below:

#### Explanation:

We can rewrite the expression as:

$\left(4.5 \times {10}^{4}\right) \left(4.5 \times {10}^{4}\right) \implies \left(4.5 \times 4.5\right) \left({10}^{4} \times {10}^{4}\right) \implies$

20.25 xx ((10^4 xx 10^4)

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

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

$20.25 \times \left({10}^{\textcolor{red}{4}} \times {10}^{\textcolor{b l u e}{4}}\right) \implies 20.25 \times {10}^{\textcolor{red}{4} + \textcolor{b l u e}{4}} \implies 20.25 \times {10}^{8}$

Now, we need to move the decimal point 1 place to the left to change this to true scientific notation:

$20.25 \times {10}^{8} \implies 2.025 \times {10}^{9}$