How do you evaluate #(6\times 10^ { 9} ) \div ( 3\cdot \times 10^ { 13} )#?

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Answer 1 · 2017-10-09T11:42:50

See a solution process below:

First, rewrite the expression as:

#(6 xx 10^9)/(3 xx 10^13) =>#

#(6/3) xx (10^9/10^13) =>#

#2 xx 10^9/10^13#

Now, use this rule of exponents to simplify the 10s terms:

#x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))#

#2 xx 10^color(red)(9)/10^color(blue)(13) =>#

#2 xx 10^(color(red)(9)-color(blue)(13)) =>#

#2 xx 10^-4#

To write this in standard form we need to move the decimal point 4 places to the left because the exponent for the 10s term is negative:

#2 xx 10^-4 => 0.0002#