Basic Rules for Exponents

EXPONENTS

Basic Rules for Exponents - h1014v1_83

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EXPONENTS Review of Introductory Mathematics Basic Rules for Exponents The following rules are applied to exponents. Rule 1: To multiply numbers with the same base, add the exponents and keep the base the same. a^maⁿ = a^m+n Example: 2² x 2³ = (2 x 2) x (2 x 2 x 2) = 2 x 2 x 2 x 2 x 2 = 2⁵ Rule 2: When raising a power of a number to a power, multiply the exponents and keep the base the same. (a^m)ⁿ = a^mn Example: (a²)³ = (a x a) x (a x a) x (a x a) = a⁶ that is, you multiply (a x a) three times. Similarly, for (a^m)ⁿ, one multiplies (a^m) n times. There are m values of a in each parenthesis multiplied by n parenthesis or m x n values of a to multiply. Thus, (a^m)ⁿ = a^mn Rule 3: When dividing two exponential numbers, subtract the powers. a^m aⁿ a^m n Example: a⁵ a² a×a×a×a×a a×a a a _×a a × a× a× a a³ MA-01 Page 62 Rev. 0

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