# How do you multiply (2x10^4)(3x10^5)?

Mar 25, 2015

I'm not sure, but I think you mean $\left(2 \times {10}^{4}\right) \left(3 \times {10}^{5}\right)$ (Use two x, 'xx' inside to get x instead of $x$

You can change the order of multiplication, so you'll multiply the parts that do not involve $10$ to a power separately from the parts that do involve $10$ to a power:

$\left(2 \times {10}^{4}\right) \left(3 \times {10}^{5}\right) = 2 \times {10}^{4} \times 3 \times {10}^{5}$

$= 2 \times 3 \times {10}^{4} \times {10}^{5}$

$= \left(2 \times 3\right) \times \left({10}^{4} \times {10}^{5}\right)$

$= 6 \times \left({10}^{4 + 5}\right)$

$= 6 \times {10}^{9}$

Here's another example that skips some steps:

$\left(3 \times {10}^{5}\right) \left(4 \times {10}^{8}\right)$

$= \left(3 \times 4\right) \times \left({10}^{5} \times {10}^{8}\right)$

$= 12 \times \left({10}^{5 + 8}\right)$

$= 12 \times {10}^{13}$

But that is not in scientific notation, so we re-write it:

$12 = 1.2 \times {10}^{1}$ So
$12 \times {10}^{13} = 1.2 \times {10}^{1} \times {10}^{13}$
$1.2 \times \left({10}^{1 + 13}\right)$

$1.2 \times {10}^{14}$