2 Properties of Exponents Product of Powers PropertyLet a be a real number, and let m and n be positive integers.To multiply powers having the same base, add the exponents.Examples**Each individual property is simple. The difficulty is keeping them straight once you have learned them all, and in remembering that the operation you perform on the exponents is not the operation that is occurring between the powers.
3 Properties of Exponents To multiply monomials, re-order the factors in order to multiply powers with like bases.I call this a training wheel step. This work can be done in your head, or by drawing arrows between the like bases on the original problem.Examples
4 Properties of Exponents Power of a Power PropertyLet a be a real number, and let m and n be positive integers.To raise a power to a power, multiply the exponents.ExamplesThis property is often confused with the product of powers property. Because of this you need to pay close attention to these two. Look at how they are related.
5 Properties of Exponents Power of a Product PropertyLet a be a real number, and let m and n be positive integers.To find a power of a product, find the power of each factor.ExamplesWhen applying all three of these rules there are multiple paths to a simplified expression.Be careful, don’t multiply the constant by the power!
6 Properties of Exponents Practice7)8)9)1)2)3)4)5)6)10)11)
7 Properties of Exponents Quotient of Powers PropertyLet a be a nonzero real number, and let m and n be positive integers such that m > nTo divide powers having the same base, subtract the exponentsWe are actually cancelling out matching factor pairs…Subtracting accomplishes the same goal with out all that work.
8 Properties of Exponents Power of a Quotient PropertyLet a and b be a real numbers with b≠0, and let m be a positive integer.To find a power of a quotient, find the power of the numerator and the power of the denominator and divide.Basic Examples:Using more than one property:Training wheels step
9 Properties of Exponents Practice1) )3)4) )6)7) )9)
10 Properties of Exponents Zero ExponentsNegative Exponentsa to the power of zero is 1.A simplified expression can not contain any negative exponents