Question

How do you simplify `\frac { 10x ^ { 2} y } { 6x ^ { 5} y ^ { 6} }`?

Answer 1

See the entire simplification process below:

Explanation:

First, rewrite the expression as:

`10/6 * x^2/x^5 * y/y^6 = (2 xx 5)/(2 xx 3) * x^2/x^5 * y/y^6 =`

`(color(red)(cancel(color(black)(2))) xx 5)/(color(red)(cancel(color(black)(2))) xx 3) * x^2/x^5 * y/y^6 = 5/3 * x^2/x^5 * y/y^6`

Now, use these two rules of exponents to complete the simplification:

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

`5/3 * x^color(red)(2)/x^color(blue)(5) * y^color(red)(1)/y^color(blue)(6) = 5/3 * 1/x^(color(blue)(5)-color(red)(2)) * 1/y^(color(blue)(6)-color(red)(1)) = 5/3 * 1/x^3 * 1/y^5 =`

`5/(3x^3y^5)`