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Rules of Exponents Assessment – 10/23/15 Topics on Exponent Assessment Product Rules When multiplying the same base, add exponents. 𝑥 4 ∙ 𝑥 5 = 𝑥 4+5 = 𝑥 9 When there is a power to a power, multiply the exponents. (𝑥 6 )5 = 𝑥 6⦁5 = 𝑥 30 When there is a power of a product, apply the exponent to each factor. (𝑥𝑦)3 = 𝑥 3 𝑦 3 Quotient Rules When dividing the same base, subtract exponents. 𝑥6 𝑥4 = 𝑥 6−4 = 𝑥 2 , 𝑥 ≠ 0 When there is a quotient to a power, distribute the exponent to everything in the numerator and denominator. 𝑥 5 𝑥5 ( ) = 5 ,𝑦 ≠ 0 𝑦 𝑦 Zero and Negative Exponents Any number to the zero power is equal to one. 𝑥 0 = 1, 𝑥 ≠ 0 Notice in this example 𝑥 ≠ 0. This because 00 is undefined. Any number to a negative power is the reciprocal of the number to a positive exponent. 1. 𝑥 −2 = 1 , 𝑥2 𝑥 ≠0 𝑜𝑟 2. 1 𝑥 −2 = 𝑥2 1 = 𝑥2 Notice in example 1 that 𝑥 ≠ 0. This is because 0 would end up in the denominator and when 0 is in the denominator it is undefined. Helpful hints Remember if you get stuck – E X P A N D! Remember the rules of exponents apply only to exponents not the bases. When multiplying the same base, add the exponents. Do not add or multiply the bases. Example: Wrong 45 ⦁49 ≠ 814 Wrong 45 ⦁49 ≠ 1614 Right 45 ⦁49 = 414 More Helpful hints When dividing the same base, subtract the exponents. Do not subtract the bases. Example: 85 83 ≠ 12 85 83 = 82 Wrong 16𝑥 7 12𝑥 2 ≠ 4𝑥 5 Right 16𝑥 7 12𝑥 2 = 4𝑥 5 3 because 16 12 simplifies to 4 3 Negative exponents do not make a positive base negative or a negative base positive. Example: Wrong 5−3 ≠ −53 Right 5−3 = Right Do not apply rules of exponents to any base. Do not subtract coefficients of fractions, simplify them. Example: Wrong 1 53 𝑜𝑟 Wrong 1 125 Right 1 (−8)−6 1 (−8)−6 ≠ = 1 86 86 1 = 86 When simplifying a more complex expression. Do it step by step applying one rule a time. 2 2 2 33𝑎6 𝑏−2 𝑐 5 3𝑎6 𝑎3 3𝑎9 32 𝑎18 9𝑎18 ( ) = ( 6 2 2 ) = ( 8 2 ) = 16 4 = 16 4 11𝑎−3 𝑏 6 𝑐 7 𝑏 𝑏 𝑐 𝑏 𝑐 𝑏 𝑐 𝑏 𝑐 Some helpful links: https://www.khanacademy.org/math/pre-algebra/exponents-radicals/World-of-exponents/v/understanding-exponents https://www.khanacademy.org/math/pre-algebra/exponents-radicals/World-of-exponents/v/understanding-exponents-2 https://www.khanacademy.org/math/pre-algebra/exponents-radicals/exponent-properties/v/exponent-rules-part-1 https://www.khanacademy.org/math/pre-algebra/exponents-radicals/exponent-properties/v/exponent-rules-part-2 https://www.khanacademy.org/math/pre-algebra/exponents-radicals/exponent-properties/e/exponent_rules https://www.khanacademy.org/math/pre-algebra/exponents-radicals/exponent-properties/e/properties-of-integerexponents https://www.khanacademy.org/math/pre-algebra/exponents-radicals/World-of-exponents/v/powers-of-zero https://www.khanacademy.org/math/pre-algebra/exponents-radicals/World-of-exponents/v/raising-a-number-to-the0th-and-1st-power https://www.khanacademy.org/math/pre-algebra/exponents-radicals/negative-exponents-tutorial/v/negativeexponents https://www.khanacademy.org/math/pre-algebra/exponents-radicals/negative-exponents-tutorial/e/exponents_2 http://www.mesacc.edu/~scotz47781/mat120/notes/exponents/review/review.html