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5.7 Rational Exponents

5.7 Rational Exponents. Objectives: Write expressions with rational exponents in radical form, and vice-versa. Simplify expressions in exponential or radical form. Rational Exponents. For any real number b and for any positive integer n, except when b<0 and n is even.

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5.7 Rational Exponents

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  1. 5.7 Rational Exponents Objectives: Write expressions with rational exponents in radical form, and vice-versa. Simplify expressions in exponential or radical form.

  2. Rational Exponents For any real number b and for any positive integer n, except when b<0 and n is even. (Any number raised to the ½ power is the same as the square root of the number etc.) Examples:

  3. Rational Exponents For any nonzero real number b and any integers m and n, with n>1, except when b<0 and n is even. Examples:

  4. Simplifying Rational Exponents To be considered simplified, the expression must meet the following conditions: • No negative exponents. • No fractional exponents in the denominator. • Not a complex fraction. • The index of any remaining radical is the least number possible.

  5. Write in radical form. Write using rational exponents. Examples:

  6. Writing Answers Should your answer be written with a rational exponent or as a radical? It depends on how the problem was written. If it starts out as a rational exponent, the answer should also be a rational exponent. If it starts out as a radical, the answer should be expressed as a radical.

  7. Simplify Examples

  8. Simplify More Examples

  9. Example Simplify

  10. Rationalizing with Binomials Rationalize:

  11. Homework Page 261 22-60 even

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