Question

How do you simplify `\frac { - 24x ^ { 5} y ^ { 3} } { 8x ^ { 2} y ^ { 8} }`?

Answer 1

This can be simplified to `(-3x^3)/y^5`.

Explanation:

This fraction is easier to solve if we break it down into many pieces. We can simplify these pieces individually and then combine them at the end.

`(-24x^5y^3)/(8x^2y^8)=(-24)/8*x^5/x^2*y^3/y^8`

First, we will solve the constant term through simply division.

`(-24)/8=-3`

Next, we will solve the `x` term.

`x^5/x^2`

When dividing exponents, we subtract the exponent of the bottom number from the exponent of the top number.

`5-2=3`

`x^3`

Now, we will solve the `y` term. We will follow the same pattern as before.

`y^3/y^8`

`3-8=-5`

`y^-5=1/y^5`

Finally, we combine all the terms.

`-3*x^3*1/y^5=(-3x^3)/y^5`