How do you simplify #(10^4)(10^9)#?

2 Answers
Alan P.
Feb 5, 2016

#(10^4)(10^9) = 10^13#

Explanation:

One way is to remember the general relation:
#color(white)("XXX")b^pxxb^q = b^(p+q)#

Or
#color(white)("XXX")10^4# means #10# multiplied together #4# times
#color(white)("XXX")#and
#color(white)("XXX")10^9# means #10# multiplied together #9# times

#color(white)("XXX")#So #10^4xx10^9# will be #10# multiplied together #13# times
#color(white)("XXX")#which can be written #10^13#

George C. · mason m
Feb 5, 2016

#(10^4)(10^9) = 10^13#

Explanation:

If #k# is a positive integer then:

#10^k = stackrel "k times" overbrace(10xx10xx...xx10)#

So if #a# and #b# are positive integers then we find:

#10^a xx 10^b = stackrel "a times" overbrace(10xx10xx...xx10) xx stackrel "b times" overbrace(10xx10xx...xx10)#

#=stackrel "a + b times" overbrace(10xx10xx...xx10)=10^(a+b)#

In our example, #a=4# and #b=9# and we find:

#(10^4)(10^9) = 10^(4+9) = 10^13#

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