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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: =

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

* Why is a equal to 1?  Simplify 25  Simplify  Quotient of powers property 5 2 – 2  Simplify  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.

Simplify: ( ) = Power of a quotient = Simplify

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

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

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

Simplify: = = = 3 13 =

Simplify: = = = = =