Question

How do you simplify `\frac { - 14x ^ { - 3} y ^ { 5} } { 35x y ^ { 3} }`?

Answer 1

`(-2y^2)/(5x^4)`

Explanation:

Recall one of the laws of indices.....`x^-m = 1/x^m`

Move the negative index and then simplify as usual.
Simplify the signs, then the numbers, then the indices.

`(-14x^-3y^5)/(35xy^3) = (-14color(blue)(y^5))/(35color(red)(x*x^3)color(blue)(y^3))`

`= (-2color(blue)(y^2))/(5color(red)(x^4))`

When dividing - subtract indices of like bases. `color(blue)(y^5/y^3 = y^2)`

When multiplying add indices of like bases. `color(red)(x xx x^3 = x^4)`