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Simplify expressions in exponential or radical form.
5.7 Rational Exponents Objectives: Write expressions with rational exponents in radical form, and vice-versa. Simplify expressions in exponential or radical form.
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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:
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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:
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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.
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Examples: Write in radical form. Write using rational exponents.
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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.
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Examples Simplify
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More Examples Simplify
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Example Simplify
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Rationalizing with Binomials
Rationalize:
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Homework Page 261 22-60 even
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