# How do you write the answer in scientific notation given (3.7times10^-5)^2?

Jun 19, 2017

See a solution process below:

#### Explanation:

We can rewrite this expression as:

${\left(3.7 \times {10}^{-} 5\right)}^{2} \implies \left(3.7 \times {10}^{-} 5\right) \times \left(3.7 \times {10}^{-} 5\right) \implies$

$\left(3.7 \times 3.7\right) \times \left({10}^{-} 5 \times {10}^{-} 5\right) \implies 13.69 \times \left({10}^{-} 5 \times {10}^{-} 5\right)$

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

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

$13.69 \times \left({10}^{\textcolor{red}{- 5}} \times {10}^{\textcolor{b l u e}{- 5}}\right) = 13.69 \times {10}^{\textcolor{red}{- 5} + \textcolor{b l u e}{- 5}} \implies$

$13.69 \times {10}^{-} 10$

To write this in true scientific notation we need to move the decimal point 1 place to the left so we can add $1$ to the exponent for the 10s term:

$13.69 \times {10}^{-} 10 \implies 1.369 \times {10}^{-} 9$