Simplify. Express using positive exponents.

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How do you simplify an expression changing the negative exponents to positive exponents?

Aug 31st, 2015

Hi there! Thank you for the opportunity to help you with your question!

A "negative exponent" is equivalent to finding the "reciprocal" of a function. In less technical terms, a negative exponent takes a number and flips it around. This is very easy to see with fractions! If I have: (3/4) raised to the -1, all you have to do is "flip it", so (3/4)^(-1) = 4/3. For numbers that are not fractions, it is a little less intuitive, but still very easy. For example, if we want to take (2)^(-1). Well, we can still think of 2 as a fraction 2/1. And then:

(2/1)^(-1) = 1/2.

Now, our expressions won't always involve things raised to the "minus 1" power. Sometimes you will have things like (5/7)^(-2). 

One way to think about this problem, is to break up the exponent into two parts, first the "negative" and then the "raised to the second power". This is easier to see if we have:


Where we used the fact that raising a number to two different powers is the same as raising the number to the product of those two powers!

Now, we know how to deal with the "minus one" power, so we get:

[7/5]^2 by flipping the fraction

And now, we know how to square a number:

[7/5]^2 = 49/25

Please let me know if you need any clarification. Always glad to help!
Sep 1st, 2015

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