1. Expand 3237 and cancel out the common 3’s and write your answer with positive exponents.
2. Evaluate 3237 by using the Quotient of Powers property.
3. Are the answers from #1 and #2 equal? Write them as a single statement.
4. Fill in the blanks. 1am=a− and 1a−m=a−
1am=a−m and 1a−m=am
From the two investigations above, we have learned two very important properties of exponents. First, anything to the zero power is one. Second, negative exponents indicate placement. If an exponent is negative, it needs to be moved from where it is to the numerator or denominator. We will investigate this property further in the Problem Set.
Simplify the following expressions. Your answer should only have positive exponents.
Solution: Use the two properties from above. An easy way to think about where the “leftover” exponents should go, is to look at the fraction and determine which exponent is greater. For example, in b, there are more x’s in the denominator, so the leftover should go there.
Alternate Method: Part c
Simplify the expressions. Your answer should only have positive exponents.
Solution: In these expressions, you will need to move the negative exponent to the numerator or denominator and then change it to a positive exponent to evaluate. Also, simplify any numerical fractions.
Multiply the two fractions together and simplify. Your answer should only have positive exponents.
Solution: The easiest way to approach this problem is to multiply the two fractions together first and then simplify.