How do you multiply #3.65×10^23# by #4.12×10^154# by #1.11×10^(−11)# and express the answer in scientific notation?

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Answer 1 · 2018-05-22T20:13:23

#= 1.669218 xx 10^167#

Consider the expression:

#3x^5 xx 4x^7 xx 8x^-9#

This could be written as: #3xx4xx8xx x^5 xx x^7 xx x^-9#

Now multiply the numbers and then add the indices of the base #x#

#= 96 x^12#

We can apply the same method with the calculation given in scientific notation:

#(3.65×10^23) xx (4.12×10^154) xx (1.11×10^(−11))#

#=(3.65 xx4.12xx1.11) xx (10^23 xx 10^154 xx 10^-11)#

Multiply the numbers and add the indices of the base #10#

#=16.69218 xx 10^166#

#= 1.669218 xx 10^167#