Summer Assignment Review Exponent Rules

Properties of Exponents Product of Powers Property Let 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.

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

Properties of Exponents Power of a Power Property Let a be a real number, and let m and n be positive integers. To raise a power to a power, multiply the exponents. Examples This 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.

Properties of Exponents Power of a Product Property Let 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. Examples When applying all three of these rules there are multiple paths to a simplified expression. Be careful, don’t multiply the constant by the power!

Properties of Exponents Practice 7)8)9) 1)2)3)4)5)6) 10)11)

Properties of Exponents Quotient of Powers Property Let a be a nonzero real number, and let m and n be positive integers such that m > n To divide powers having the same base, subtract the exponents We are actually cancelling out matching factor pairs… Subtracting accomplishes the same goal with out all that work.

Properties of Exponents Power of a Quotient Property Let 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

Properties of Exponents Practice 1) 2)3) 4) 5)6) 7) 8)9)

Properties of Exponents Zero Exponents Negative Exponents a to the power of zero is 1. A simplified expression can not contain any negative exponents

Properties of Exponents Practice