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3. Let a be a real number and m and n be integers, Then: = Let a be a real number and m and n be integers, Then: = Let a and b be real numbers and m be an integer, Then: = Let a be a nonzero real number, Then: =

4. Let a be any real number and m and n be integers, Then: = Let a and b be real numbers and n be an integer, Then: = Let a be any real number and n be an integer, Then: = Note: a ≠ 0 Note: b ≠ 0 = and Note: a ≠ 0

5. * Why is a equal to 1? 0 5 5 2 2  Simplify 25  Simplify 1 5 5 2 2  Quotient of powers property 5 2 – 2  Simplify 5 0 1  Zero exponent property The zero exponent property is a result of the quotient of powers property. For Quotient of powers property to work, we derive the zero exponent property for this special case.

6. Simplify: ( ) 11 7 7 = 2 2 2 Power of a quotient = 49 121 Simplify

7. Simplify: = 6 6 5 7 Quotient of powers 6 5 – 7 Simplify 6 − 2 6 2 1 Negative exponent = = = = Simplify 36 1

8. ( ) y x Simplify: x y = = y x = = = = 1 Product of powers Quotient of powers Zero Exponent

9. Simplify: 3 ab 6 a b -5 7 Quotient of powers Divide Negative exponents = = = = Simplify 9 ab 2 a b -5 7 9 a 2 b 2 2 a b -5 - 1 9 - 7 2 a b -6 2 6

10. Simplify: = = - 5 3 2 - 4 7 - 5 7 = 3 13 =

11. Simplify: = = = = =