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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So 5 to the -2. What that tells me is that this term which is in the numerator right now this is 5 to the -2 over 1 is just going to have to move down to the denominator leaving me with 1 over 5² which is the same thing as 1 over 25.

Similarly when we have a negative exponent in the denominator it just moves it to the denominator, so this ends up being 4² which is going to be 16 and what a negative does on a fraction is just basically flip it over. There's a number of different ways you could deal with this problem. You could distribute this -3 in, we have a fraction to a power, this -3 has to go both the numerator and the denominator or you could just say okay this is 2/3 to the -1 to the third.

Basically remember when you have a power to a power you have to multiply so -1 to the third is the same thing as -3. What this -1 does is flip over my fraction so what I have here then is, 3/2 to the third, this 3/2 will get distributed into both leaving us with 3 to the third, 27 over 2 to the third which is 8.

Like I said you could also distribute this in so you'd end up with 2 to the -3, the negative is going to bring it down to the denominator leaving us with 2 to the third. We'd also have 3 to the -3 in the denominator and they would bring it up to the top leaving us with the 3 to the third in the top or 27.

A number of different ways of dealing with this, what I tend to do is if I see a negative sign on a fraction or a statement I just know that everything is going to have to get flipped to the opposite spot, but if you want to distribute it in first that's perfectly fine too.