# Math Help - Evaluate using scientific notation.

1. ## Evaluate using scientific notation.

Using scientific notation, evaluate:

(4 x 10^8)^3 divided by (5 x10^-6)^2

Do I just convert this to 40 x 10^11 divided by 50 x 10^-4?

If so..

then I divide 40 by 50, which is .8

So we got .8 x 10^7 as the answer.

Am I doing this right? thanks.

2. Originally Posted by hansbethe

Using scientific notation, evaluate:

(4 x 10^8)^3 divided by (5 x10^-6)^2

Do I just convert this to 40 x 10^11 divided by 50 x 10^-4?

If so..

then I divide 40 by 50, which is .8

So we got .8 x 10^7 as the answer.

Am I doing this right? thanks.

$\frac{(4\cdot 10^8)^3}{(5\cdot 10^{-6})^2}$

$= \frac{4^3\cdot (10^8)^3}{5^2\cdot (10^{-6})^2}$

$= \frac{64\cdot 10^{24}}{25 \cdot 10^{-12}}$

$= \frac{64}{25}\cdot 10^{24 - (-12)}$

$= \frac{64}{25}\cdot 10^{36}$

$= \left(\frac{8}{5}\right)^2\cdot (10^{18})^2$

$= \left(\frac{8}{5}\cdot 10^{18}\right)^2$.