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
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