How do you evaluate #\frac { ( 8.6\times 10^ { - 3} ) \times ( 3.9\times 10^ { - 6} ) } { ( 3.6\times 10^ { - 7} ) \times ( 4.3\times 10^ { - 3} ) }#?

1 Answer
smendyka
Dec 5, 2017

See a solution process below:

Explanation:

First, rewrite the expression as:

#(8.6 xx 3.9)/(3.6 xx 4.3) xx (10^-3 xx 10^-6)/(10^-7 xx 10^-3) =>#

#(2 xx 4.3 xx 3 xx 1.3)/(3 xx 1.2 xx 4.3) xx (10^-3 xx 10^-6)/(10^-7 xx 10^-3) =>#

#(2 xx color(red)(cancel(color(black)(4.3))) xx color(blue)(cancel(color(black)(3))) xx 1.3)/(color(blue)(cancel(color(black)(3))) xx 1.2 xx color(red)(cancel(color(black)(4.3)))) xx (color(green)(cancel(color(black)(10^-3))) xx 10^-6)/(10^-7 xx color(green)(cancel(color(black)(10^-3)))) =>#

#(2 xx 1.3)/(1.2) xx 10^-6/10^-7 =>#

#(2 xx 1.3)/(2 xx 0.6) xx 10^-6/10^-7 =>#

#(color(red)(cancel(color(black)(2))) xx 1.3)/(color(red)(cancel(color(black)(2))) xx 0.6) xx 10^-6/10^-7 =>#

#2.1bar6 xx 10^-6/10^-7#

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

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

#2.1bar6 xx 10^color(red)(-6)/10^color(blue)(-7) =>#

#2.1bar6 xx 10^(color(red)(-6)-color(blue)(-7)) =>#

#2.1bar6 xx 10^(color(red)(-6)+color(blue)(7)) =>#

#2.1bar6 xx 10^1#

Or

#2.1bar6 xx 10#

Or

#21.bar6#

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