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Rules of Exponents - Problem 2

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Teacher/Instructor Carl Horowitz
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!

Using the rules of exponents to simplify an expression with negative exponents. So the main thing you have to remember when dealing negative exponents is it basically takes anything that is in the numerator, puts in the denominator, anything that's in the denominator and moves it to the numerator.

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.

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