# How to simplify (9 times10^ -31) xx (3times10 ^7)^2  in scientific notation?

May 14, 2018

$8.1 \times {10}^{-} 16$

#### Explanation:

$\left(9 \times {10}^{-} 31\right) \times \left(3 \times {10}^{7}\right) 2$

$9 \times {10}^{-} 31 \cdot 9 \times {10}^{14}$

$\left(9 \times 9\right) \cdot \left({10}^{-} 31 \times {10}^{14}\right)$

$\left(81\right) \cdot \left({10}^{- 31 + 14}\right)$

$81 \times {10}^{-} 17$

note that in scientific notation, numbers are between $1 \mathmr{and} 10$ so $81$ is not included

so move the decimal point to the left
when you move it to the left you have to multiply by 10

$81 = 8.1 \times 10$

simplify $8.1 \times 10 \times {10}^{-} 17$

$\textcolor{red}{{10}^{-} 17 \times 10 = {10}^{-} 16}$

$8.1 \times {10}^{-} 16$