Working with exponents unit
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This document outlines several rules for working with exponents. It provides rules for the power of a power, power of a product, product of powers, power of a quotient, quotient of powers, zero as a power, powers of -1, and negative exponents. Examples are given to illustrate each rule.
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Working with exponents unit
- 1. WORKING WITH EXPONENTS RULES POWER OF A POWER PROPERTY Rule: (ab)c = a(b*c) Example: (x3)4 = x(3*4) = x12 POWER OF A PRODUCT PROPERTY Rule: (a * b)c = ac * bc Example: (2b)3 = 23 * b3 = 8b3 PRODUCT OF POWERS PROPERTY Rule: ab * ac = a(b+c) Example: a4 * a5 = a(4+5) = a9 POWER OF A QUOTIENT PROPERTY Rule: (a/b)c = ac / bc Example: (2/3)3 = (23/33) = 8/27 QUOTIENT OF POWERS PROPERTY Rule: ab / ac = a(b-c) Example: z5 / z3 = z(5-3) = z2 ZERO AS A POWER Rule: a0 = 1 Example: 40 = 1 POWERS OF -1 Rule: Even powers of -1 = 1 Example: (-1)8 = 1 Rule: Odd Powers of -1 = -1 Example: (-1)13 = -1 NEGATIVE EXPONENTS Rule: (a-b) = 1/(ab) Example: (5-2) = 1/(52) = 1/25