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Rational Exponents MATH 017 Intermediate Algebra S. Rook

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2 Overview Section 7.2 in the textbook –Simplify rational exponents –Apply rational exponents to simplify rational expressions

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Simplify Rational Exponents

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4 Rational Exponents Thus far, we have only seen integer exponents –Ex: 5 3, x -5 Possible to have rational (i.e. fractional) exponents –Ex: 8 1/3, y -3/4

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5 Rational Exponents vs Radical Notation Relationship between rational exponents and radical notation where p is power and r is radical Ex: Most calculators take only up to the third root –How would we evaluate

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6 Rational Exponents vs Radical Notation (Example) Ex 1: Use radical notation to write the following and simplify if possible

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7 Rational Exponents vs Radical Notation (Example) Ex 2: Use radical notation to write the following and simplify if possible

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8 Negative Rational Exponents Write any negative rational exponents as positive rational exponents Apply radical notation and simplify if possible

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9 Rational Exponents vs Radical Notation (Example) Ex 3: Use radical notation to write the following and simplify if possible. Leave NO negative exponents

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Simplify Rational Exponent Expressions

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11 Simplify Rational Exponent Expressions Exponent rules for integer exponents apply to rational exponents as well –Remember them? Product: x a ∙ x b = x a+b Quotient: x a / x b = x a-b Power: (x a ) b = x ab

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12 Simplify Rational Exponent Expressions (Example) Ex 4: Use the properties of exponents to simplify – write with only positive exponents

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13 Simplify Rational Exponent Expressions (Example) Ex 5: Use the properties of exponents to simplify – write with only positive exponents

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14 Simplify Rational Exponent Expressions (Example) Ex 6: Use the properties of exponents to simplify – write with only positive exponents

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15 Simplify Rational Exponent Expressions (Example) Ex 7: Use the properties of exponents to simplify – write with only positive exponents

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16 Simplify Rational Exponent Expressions (Example) Ex 8: Use rational exponents to simplify the following – leave the final answer in radical notation

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17 Summary After studying these slides, you should know how to do the following: –Understand rational exponents. This includes being able to convert to radical notation and simplify –Simplify expressions containing rational expressions using the exponent rules

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