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Negative Exponents and Zero ExponentsSo far in this unit, you've learned how to simplify monomial expressions with positive exponents. Now we are going to study two more aspects of monomials: those that have negative exponents and those that have zero as an exponent. I am going to let you investigate to see if you can come up with the rule on your own! Take a look at the following problems and see if you can determine the pattern.
Can you figure out the rule? If not, here it is... The Rule for Negative Exponents:The expression a-n is the reciprocal of an TIP:A reciprocal is when you "flip a fraction". Examples: The reciprocal of 3/4 is 4/3. The reciprocal of 5 is 1/5. (You can make a whole number a fraction by putting a one in the denominator: 5 = 5/1) ***An easy rule to remember is: if the number is in the numerator (top), move it to the denominator (bottom). If the number is in the denominator, move it to the numerator! Let's take a look at a couple of examples: Examples
Now let's quickly take a look at monomials that contain the exponent 0. Any number (except 0) to the zero power is equal to 1.
Not too hard, is it? Let's look at a couple of example problems and then you can practice a few! Example 1
Example 2
**Since 2/3 is in parenthesis, we must apply the power of a quotient property and raise both the 2 and 3 to the negative 2 power. First take the reciprocal to get rid of the negative exponent. Then raise (3/2) to the second power. Example 3
Example 4
Yes, I know that's a lot of examples to comprehend. My goal was to start easy and progress to harder problems. Are you ready to try a few on your own? Practice Problems
Answer Key
So, how did you do? Are you ready to move onto Scientifc Notation? Exponents & Monomials Unit |
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