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

1 Answer
Mar 25, 2015

I'm not sure, but I think you mean (2xx10^4)(3xx10^5) (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:

(2xx10^4)(3xx10^5)=2xx10^4xx3xx10^5

=2xx3xx10^4xx10^5

=(2xx3)xx(10^4xx10^5)

=6xx(10^(4+5))

=6xx10^9

Here's another example that skips some steps:

(3xx10^5)(4xx10^8)

=(3xx4)xx(10^5xx10^8)

=12xx(10^(5+8))

=12xx10^13

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

12=1.2xx10^1 So
12xx10^13=1.2xx10^1xx10^13
1.2xx(10^(1+13))

The final answer is:
1.2xx10^14