7'2 Properties of Rational Exponents

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7.2 Properties of Rational Exponents
7.2 Properties of Rational Exponents
7.2 Properties of Rational Exponents
7.2 Properties of Rational Exponents
7.2 Properties of Rational Exponents
7.2 Properties of Rational Exponents
7.2 Properties of Rational Exponents
7.2 Properties of Rational Exponents
7.1
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Section Terms
Properties of Integers in 6.1 can also be applied
to rational exponents
6.1

• Terms
• Simplest form- a radical expression after you
  apply the properties of radicals, remove any
  perfect nth powers, and rationalize any
  denominators.
• Like radicals- two radicals expressions that have
  the same radicand.

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Section Facts
6.1
Properties of Rational Exponents

• am an amn
• (am)n a(m)(n)
• (ab)m am bm
• a-m 1/am, a ? 0
• am/an am-n, a ? 0
• (a/b)m am/bm, b ? 0
• (examples on pg 407)

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Walk Through Problems

• ³????³? (272) Factor out product cube
• ³?27 ³?2 Product property
• 3 ³?2 Simplify
• 5?3/4 5?(3 8)/(4 8)Make the denominator a
  perfect fifth power
• 5?24/32 Simplify
• (5?24)/ (5? 32) Quotient Property
• (5?24)/2 Simplify

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Summary of 7.1
Real nth roots

• Let n be an integer greater that 1 and let a be a
  real number
• If n is odd, then a has one real nth root
  n?aa(1/n)
• If n is even and a 0, then a has two n roots
• ? n?a ? a(1/n)
• If n is even and a 0, the a has one n root
  n?00(1/n)0
• If n is even and a 0, then a has no real nth
  roots.

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6.1 Properties of Exponents

• Product of Powers Property- am an amn
• Power of a Power Property- (am)n a(m)(n)
• Power of a Product Property-(ab)m am bm
• Negative Exponent Property- a-m 1/am, a ? 0
• Zero Exponent Property- a0 1, a ? 0
• Quotient of Powers Property- am/an am-n, a ?
  0
• Power of a Quotient- (a/b)m am/bm, b ? 0