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Section 7.6: Rational Exponents

Section 7.6: Rational Exponents. CP Algebra II. Rational Exponents. For any real number b and any positive integer n , Except when and n is even. When this happens, a complex root may exist. Write in radical form. Write in exponential form. . Rational Exponents.

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Section 7.6: Rational Exponents

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  1. Section 7.6: Rational Exponents CP Algebra II

  2. Rational Exponents • For any real number b and any positive integer n, • Except when and n is even. When this happens, a complex root may exist. • Write in radical form. • Write in exponential form.

  3. Rational Exponents • For any nonzero number b, and any integers x and y, with • Except when and y is even. When this happens, a complex root may exist. • Example:

  4. Properties of Rational Exponents • When simplifying expressions that contain rational exponents, the rules of exponents still apply. • Product of Powers • Quotient of Powers • Negative Exponents • Power of a Power • Power of a Product • Power of a Quotient • Zero Power • See Section 6.1 notes for examples

  5. Expressions with Rational Exponents • An expression with rational exponents is simplified when all of the following conditions are met: • It has no negative exponents • It has no fractional exponents in the denominator • It is not a complex fraction • The index of any remaining radical is the least number possible

  6. Examples • Simplify

  7. Simplify

  8. Homework • Section 7.6: pg. 450 (16-39)

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