# How do you multiply (3.00xx10^(17))xx(6.63xx10^(-34))?

May 11, 2018

(3.00xx10^17)xx(6.63xx10^(-34))=color(blue)(1.99xx10^(-16)

Refer to the explanation for the process.

#### Explanation:

Given:

$\left(3.00 \times {10}^{17}\right) \times \left(6.63 \times {10}^{- 34}\right)$

Multiply the coefficients.

$3.00 \times 6.63 \times {10}^{17} \times {10}^{- 34}$

Simplify $3.00 \times 6.63$ to $19.9$. $\leftarrow$ three significant figures

$19.9 \times {10}^{17} \times {10}^{- 34}$

Apply product rule: ${a}^{m} {a}^{n} = {a}^{m + n}$

$19.9 \times {10}^{17 + \left(- 34\right)}$

Simplify.

$19.9 \times {10}^{- 17}$

To convert the answer to scientific notation, move the decimal to the left one place and add $1$ to the exponent.

$19.9 \times {10}^{- 17} = 1.99 \times {10}^{- 16}$