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

1 Answer
Jim H · Meave60
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#

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