How do you multiply #(6.3\times 10^ { - 5} ) ( 3.4\times 10^ { 8} )#?

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Answer 1 · 2017-06-10T20:47:57

#2.142 xx 10^4#

Consider multiplication in Algebra:

#3x^8 xx 5x^4 = 3xx5 xx x^8 xx x^4#

#=15 x^(8+4)) = 15x^12#

Add the indices of like bases.

#9x^-4 xx 3x^7 = 9xx 3 xx x^-4 xx x^7#

#=27x^((-4+7)) =27x^3#

It works exactly the same in scientific notation:

#6.3 xx 10^-5 xx 3.4 xx 10^8#

#= 6.3xx3.4 xx 10^-5 xx 10^8#

#=21.42 xx 10^((-5+8))#

#=21.42 xx 10^3#

Change to correct scientific notation with one digit before the decimal point.

#=21.42 xx 10^3 = 2.142 xx 10^4#