Hi,

How do I simplify and state the restrictions on the following:

12x^8y^9 / 3x^4y^6

what do I need to factor out? I'm so confused, I never know what I'm allowed to factor out.

(12/3) (x^8/x^4)(y^9/y^6)

4 * x^4 * y^3

you can remove (cancel)common factors from the numerator and denominator

... like 3 , x^4 , and y^6

leaving ... 4 x^4 y^3
... this expression has no restrictions

BUT ...
the original expression had variables in the denominator (that were cancelled)
... these variables cannot be zero
... division by zero is a BIG no-no

if you graph the original expression, there will be holes where x and/or y equal zero
... because the numerator and denominator both equal zero

Thank you! That helped me a lot and I understand it now.

To simplify the expression 12x^8y^9 / 3x^4y^6, you need to divide the numerical coefficients and subtract the exponents of the variables.

Step 1: Divide the numerical coefficients: 12 / 3 = 4.

Step 2: Divide the variables with the same base and subtract the exponents: x^8 / x^4 = x^(8-4) = x^4, and y^9 / y^6 = y^(9-6) = y^3.

So, the simplified form of the expression is 4x^4y^3.

Now, let's talk about the restrictions. In this context, restrictions generally refer to any values of the variables that would make the expression undefined or result in division by zero.

In this case, there are no specific restrictions since there are no denominators involved in the expression. You can substitute any real values for x and y, and the expression will be defined.

Therefore, there are no restrictions in terms of values for x and y.