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Published byDominic Wood Modified over 9 years ago
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1 Notice what happens when you multiply two powers with the same base. a 4 a 3 = ( a a a a ) ( a a a ) = 4 factors 3 factors 7 factors This example suggests a rule for multiplying powers with the same base. a 4 + 3 =a 7a 7 Rules of Exponents 4.5 LESSON
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2 Product of Powers Property To multiply powers with the same base, add their exponents. Words Algebra a m a n = a m + n Numbers 4 3 4 2 = 4 3 + 2 = 4 5 Rules of Exponents 4.5 LESSON
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3 Using the Product of Powers Property EXAMPLE 1 Lake Powell Lake Powell, the reservoir behind the Glen Canyon Dam in Arizona, can hold about 10 12 cubic feet of water when full. There are about 10 27 water molecules in 1 cubic foot of water. About how many water molecules can the reservoir hold? = 10 12 10 27 Product of powers property = 10 39 = 10 12 + 27 ANSWER Lake Powell can hold about 10 39 molecules of water. Substitute values. Add exponents. SOLUTION Number of water molecules in reservoir = Cubic feet of water in reservoir Number of water molecules in a cubic foot Rules of Exponents 4.5 LESSON
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4 Using the Product of Powers Property EXAMPLE 2 = 3 5 x 6 Multiply. = 15x 6 Add exponents. = 3 5 x 1 + 5 Product of powers property 3 5 x 1 x 5 Commutative property of multiplication 3x 5x 5 = Rules of Exponents 4.5 LESSON
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5 Quotients of Powers There is a related rule you can use for dividing powers with the same base. The following example suggests this rule. 5 factors 2 factors a a a = a 5 – 2 = a 5a 5 = a 2a 2 a a a a a a = a a a a a a 11 11 = 3 factors a 3 Rules of Exponents 4.5 LESSON
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6 Quotient of Powers Property To divide powers with the same base, subtract the exponent of the denominator from the exponent of the numerator. Words Algebra Numbers a ma m = a m – n, where a ≠ 0 a na n = 6 8 – 5 = 6 3 6 86 8 6 56 5 Rules of Exponents 4.5 LESSON
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7 Using Both Properties of Powers EXAMPLE 3 Subtract exponents. Quotient of powers property Divide numerator and denominator by 3. Simplify. 3m 5 m 2 6m 36m 3 Add exponents. Product of powers property = 3m 5 m 2 6m 36m 3 3m 5 + 2 6m 36m 3 = 3m 73m 7 6m 36m 3 = 3m 7 – 3 6 = 3m 43m 4 6 = m 4m 4 2 Rules of Exponents 4.5 LESSON
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8 Easy Way to Learn the Rules of Exponents http://www.mathsisfun.com/algebra/exponent- laws.html
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