Carl Horowitz

**University of Michigan**

Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

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Whenever we have more than one term to a power, that power has to get distributed into everything, so I know that this 2 has to come in to both the x and the y and this 3 has to come in to both the x and the z. The 5 stays as it is and then we have x² squared, when you have a power to a power you have to multiply so this turns out to be x to the fourth. Y to the first squared that just turns into y² and then z stays on the outside.

10 stays on the outside as well, xz to the third there's no powers on either x or z, so we end up with just a single x³ and z³ and then the y on the outside.

Now we have to simplify. So the numeric part is the easy part, we have 5 over 10 that just cancels into 1 over 2, so we know we have a 2 in the denominator. Then I have to pair up our xs, our ys, and our zs. We have x to the fourth over x to the third. When we are dividing, I know I have to subtract my power when the numerator is larger than the denominator so that tells me I'm going to have my term left with numerator, 4 minus 3 is 1, so I just have a single x in the numerator.

Going on to the ys, y² over y again division we can subtract there's a little imaginary 1 here, so our numerator wins out, 2 minus 1 is 1 we end up with just a single y in the numerator.

And our last is our z, we have a single z in the numerator and 3z's in the denominator so 1 minus 3 is -2, the negative tells me that it's going to be in the denominator so we have a z² in the bottom.

So using our rules of exponents, we were able to expand this out and make it a little bit ugly, but then combine all our like terms just using our tricks from division.