Question

How do you simplify `\frac { - 16r ^ { 3} y ^ { 2} } { - 4r ^ { 2} y ^ { 7} }`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`(-16)/-4(r^3/r^2)(y^2/y^7) => 4(r^3/r^2)(y^2/y^7)`

Next, use these two rule of exponents to simplify the `r` and `y` 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))`

`4(r^color(red)(3)/r^color(blue)(2))(y^color(red)(2)/y^color(blue)(7)) => 4(r^(color(red)(3)-color(blue)(2)))(1/y^(color(blue)(7)-color(red)(2))) = 4(r^1)(1/y^5) = (4r^1)/y^5`

Now, use this rule of exponents to complete the simplification of the `r` term:

`a^color(red)(1) = a`

`(4r^color(red)(1))/y^5 = (4r)/y^5`