Question

How do you solve `\frac { 4x ^ { - 3} y ^ { 2} } { 6x ^ { - 5} y ^ { - 1} }`?

Answer 1

See the entire solution process below:

Explanation:

First, rewrite the expression as:

`(4/6)(x^-3/x^-5)(y^2/y^-1) => ((2 xx 2)/(2 xx 3))(x^-3/x^-5)(y^2/y^-1) =>`

`((color(red)(cancel(color(black)(2))) xx 2)/(color(red)(cancel(color(black)(2))) xx 3))(x^-3/x^-5)(y^2/y^-1) => (2/3)(x^-3/x^-5)(y^2/y^-1)`

We can now use this rule of exponents to complete the solution:

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

`2/3(x^color(red)(-3)/x^color(blue)(-5))(y^color(red)(2)/y^color(blue)(-1b)) = 2/3x^(color(red)(-3)-color(blue)(-5))y^(color(red)(2)-color(blue)(-1)) =`

`2/3x^(color(red)(-3)+color(blue)(5))y^(color(red)(2)+color(blue)(1)) =`

`2/3x^2y^3`