Did you know that the Rule of Exponents for Division is the opposite of the Rule of Exponents for Multiplication?
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
When you multiply like bases we add exponents; with division we subtract exponents!
In other words, to divide exponents (or powers) with like bases all you have to do is subtract the exponents!
But the order of subtraction is very, very important!
The exponent in the numerator (top) must come first!
Always think…
…top minus bottom
But what happens if the exponent in the denominator (bottom) is bigger than the exponent on the top? Wouldn’t this create a Negative Exponent?
Yes.
So what do we do with negative exponents?
Well, we need the Rule for Negative Exponents.
As we will see in the video, to make negative exponents positive, all we have to do is “flip” the fraction.
Negative Exponent Rule
This is nothing more than moving the base of our exponential expression from the top to the bottom, or vise-versa, and changing the exponent from negative to positive.
Why?
Zero Exponent Property
Because a negative exponent is just a nice way of saying, “Hey, I’m on the wrong side of the division bar (fraction line).”
Don’t worry; it will all make sense after you see a few examples!
Moreover, together we are going to review our cancellation rule for fractions (or the Property of Quotients) and revisit how to use the Zero Exponent Rule, and write expressions only using positive exponents so we can become champions of Monomial Division.
Negative Exponents – Video
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