MAT 150 Unit 11

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MAT 150 Unit 11

• Ch 11 1
• Working with Exponents

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Section 11 1 Laws of Exponents

• An exponent or power tells you how many times to
  use the base as a factor.
• Ex 1. In 42 the 4 is the base and 2 is the power
• it means 4(4).
• Ex 2. 65 means 6(6)(6)(6)(6).
• Ex 3. X3 means X(X)(X)

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Section 11 1 Laws of Exponents

• Multiplying powers of the same base
• 23 (22) 2(2)(2)(2)(2) 25
• x4 x2 x(x)(x)(x)(x)(x) x6
• So rather than expand each power and count the
  factors we have
• Rule 1 To multiply powers with like bases add
  the exponents
• am(an) amn a 0

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Section 11 1 Laws of Exponents

• Dividing powers with like bases
• x5 x(x)(x)(x)(x) x(x)(x)(x)(x) x(x)(x)
  x3
• x2 x(x) x(x)
• 37 3(3)(3)(3)(3)(3)(3)
  3(3)(3)(3)(3)(3)(3) 34
• 33 3(3)(3)
  3(3)(3)
• w2 w(w) 1
• w4 w(w)(w)(w) w2
• So rather than expand each power, cancel and
  count we have
• Rule 2 To divide powers with like bases
  subtract the exponents
• am am-n
• an a 0

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Section 11 1 Laws of Exponents

• More on dividing exponents
• Using the rule x2 x2 5 x 3 or 1
• x5
  x3
• So a negative exponent means 1 over the base.
• Ex1 a a1 4 a 3 or 1
• a4 a3
• Ex2 x3 x3 ( 5) x35 x8
• x 5
• Ex3 22 22 2 20 but 4 1
• 22
  4
• Things to remember
• N 1 1 and N0 1
• N

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Section 11 1 Laws of Exponents

• Finding a power of a power
• (32)3 (32)(32)(32) 3222 36
• (x3)5 (x3)(x3)(x3)(x3)(x3) x33333 x15
• So again, rather than expand raising a power to a
  power we have
• Rule 3 When raising a power to a power,
  multiply the exponents.
• (am)n amn

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Section 11 1 Laws of Exponents

• Raising a fraction or quotient to a power
• (½)3 (½)(½)(½) 13/23 1/8
• Rule4 When raising a fraction or quotient to a
  power raise the numerator to the power and the
  denominator to the power.
• (a/b)n an/bn
• Watch for using multiple rules
• (x2/y3)4 (x2)4/(y3)4 x8/y12

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Section 11 1 Laws of Exponents

• Raising a product to a power
• (ab)2 abab aabb a2b2
• (3x)3 (3x)(3x)(3x) 33x3 27x3
• Rather than expanding we can use
• Rule5 When raising a product to a power, raise
  each factor to the power.
• (ab)n anbn

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Section 11 1 Laws of Exponents

• Rule 1 To multiply powers with like bases add
  the exponents
• am(an) amn a 0
• Rule 2 To divide powers with like bases
  subtract the exponents
• am am-n
• an a 0
• Also N 1 1 and N0 1
• N

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Section 11 1 Laws of Exponents

• Rule 3 When raising a power to a power,
  multiply the exponents.
• (am)n amn
• Rule4 When raising a fraction or quotient to a
  power raise the numerator to the power and the
  denominator to the power.
• (a/b)n an/bn
• Rule5 When raising a product to a power, raise
  each factor to the power.
• (ab)n anbn