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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First one is our bases are the same and we are multiplying which tells us we have to add our exponents so what we end up with is y to the 4 plus 2 or y to the sixth.

Second example we are dividing, when we're dividing we end up subtracting and what I see is that my degree in the bottom, the power in the bottom is larger than the power on the top, so I actually know that I'm going to have to end up with a term in the bottom and then just 4 minus 7 is -3, the negative tells me this is in the bottom so it's just going to be x³. Another way of writing this if you want to deal with negative exponents could be x to the -3.

Third one is z to the third to the fifth, we have a power to a power, I know I have to multiply so what I end up with is z to the 3 times 5 which is just z to the 15th.

And the last one is we're dealing with expression to a power. This 4 has to get distributed in which tells me and then when I have the x² to the fourth, this has to be multiplied so ending up with x to the eighth and then we have y to the fourth stands alone. So using our rules of exponents to simplify an expression.