Question

How do you simplify `\frac { 7b ^ { - 3} a ^ { 2} } { 6a ^ { - 3} b ^ { 2} }`?

Answer 1

See the entire simplification process below:

Explanation:

First, rewrite this expression as:

`(7/6)(a^2/a^-3)(b^-3/b^2)`

Now, use these rules of exponents to simplify the `a` and `b` terms:

`x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))` and `x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))`

`(7/6)(a^color(red)(2)/a^color(blue)(-3))(b^color(red)(-3)/color(blue)(b^2)) = (7/6)(a^(color(red)(2)-color(blue)(-3)))(1/b^(color(blue)(2)-color(red)(-3))) =`

`7/6(a^(color(red)(2)+color(blue)(3)))(1/b^(color(blue)(2)+color(red)(3))) = 7/6(a^5)(1/b^5) = (7a^5)/(6b^5)`