Rational Exponents

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Rational Exponents
Prof. Ahlee Aleeman
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What are Rational Exponents?

• Exponents that are fractions
• The properties of rational exponents are the same
  for properties for integer exponents.

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Definitions of

• If represents a real number and n 2 is
  an integer then
• If n is even, a must be nonnegative.
• If n is odd, a can be any real number.
• Note note the denominator and the index.

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Radical Notation, Exponential Notation

• Radical Notation Radical sign is used.
• Example 3????
• Exponential Notation Exponents are used.
• Example 4 1 3

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Using the definition

• Use radical notation to rewrite the expression.
  Simplify, if possible

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Check the definition again.

• or
• Radicals index becomes the exponents
  denominator.
• Radicand become the base.

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Rewrite with rational exponents

• b)

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Observe

• what do you notice?

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Definition of

• and
• Numerator of the exponent become the exponent of
  the base
• Denominator of the exponent become the root
  index.

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Use the definition

• Use radical notation to rewrite and simplify.

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Rewrite with rational exponents

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Rewrite with positive exponents and simplify

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An expression with rational exponents is
simplified when

• No parentheses appear.
• No powers are raised to powers.
• Each base occurs only once.
• No negative or zero exponents appear.

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Properties of Rational Exponents Page 519

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Simplify completely

• b)
• c)

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Simplify completely. Use rational exponents

• b)
• c)

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Summary

• Rational exponent
• exponent denominator is the root index
• ?? ?? ?? ?? ?? ??
• radical expression
• root index is the denominator of the fractional
  exponent
• ?? ?? ?? ?? ?? ??

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End of Slides