Exponents are often used as a shorthand way to show repeated multiplication, so you can expect to encounter several questions on the TASC Math exam that involve exponents.

You can apply the following general rules about exponents:

  • Zero exponent rule: Any number raised to the zero power is equal to 1.
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  • Product rule: When multiplying numbers with the same base, add the exponents.
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  • Power rule: When raising a power to a power (inside/outside exponents), multiply the exponents.
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  • Quotient rule: When dividing numbers with the same base, subtract the exponent of the denominator from the exponent of the numerator.
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  • Negative exponent rule 1: A negative exponent in the numerator indicates that part of the term belongs in the denominator.
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  • Negative exponent rule 2: A negative exponent in the denominator indicates that part of the term belongs in the numerator.
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  • Negative exponent rule 3: When raising an entire quotient to a negative exponent, you can "flip" the fraction (use the reciprocal).
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  • Distribution rule 1: When raising an entire product to a power, distribute the exponent to each part of the product.
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  • Distribution rule 2: When raising an entire quotient to a power, distribute the exponent to each part of the quotient.
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Keep in mind that you should never distribute over addition or subtraction! For example,

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it really means (x + y)2 = (x + y)(x + y).

Practice questions

  1. Which is equivalent to (x2)1/3?
    TASC_1111
  2. Simplify 3(20 + 52). A. 21 B. 31 C. 75 D. 78

Answers and explanations

  1. The correct answer is Choice (C). Using the power rule for exponents you multiply the inside/outside exponents. Multiplying the exponents results in
    TASC_1112
    which means the answer is Choice (C), x2/3.
  2. The correct answer is Choice (D). You should notice that you must use both the order of operations and the exponent rules. Recall that anything to the 0 power is 1, so using the exponent rules you get 3(1 + 25) = 3(26) = 78, which is Choice (D). Choices (A) and (C) result from applying the 0 exponent rule incorrectly.

About This Article

This article is from the book:

About the book authors:

Stuart Donnelly, PhD, earned his doctorate in mathematics from Oxford University at the age of 25. Since then, he has established successful tutoring services in both Hong Kong and the United States and is considered by leading educators to be one of the most experienced and qualified private tutors in the country. Nicole Hersey, PhD, is a lecturer at the University of Rhode Island, with a dual appointment to the School of Education and the Department of Mathematics. Ron Olson, MA, is an NBCT-certified teacher in Social Studies who teaches AP Government, Civics, and Contemporary World Problems at Clover Park High School in Lakewood, WA. In addition to his 35 years of teaching experience, he works as an AP US History workshop consultant for The College Board and has been the advisor for National Honor Society at his high school. Shannon Reed, MA, MFA, is a visiting lecturer at the University of Pittsburgh, where she teaches composition, creative writing, and business writing.

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