Fractional Exponents and Radicals

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Fractional Exponents and Radicals

• Section 0.3

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Radical Expressions

• is a radical expression
• ? is the radical sign
• a is the radicand
• n is the index (or the order) of the radical

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Examples of Radicals
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Perfect Squares

• Squares of Positive Integers
• 1, 4, 9, 16, 25, 36, 49, 64,81, 100, 121,144,
  169, 196, 225, 256, 289, 324,381,400
• Perfect Square Expressions
• x2, x4, x6, x8, ...

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Perfect Cubes

• Cubes of Positive Integers
• 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000
• Perfect cube expressions
• x3, x6, x9, x12, x15, ...

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Radicals involving variables
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Simplify Radicals
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Combine Like RadicalsLike Radicals Radicals
with the same index and same radicand
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Rationalizing the Denominator
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Rationalize the numerator
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Fractional Exponents with Nonnegative Bases

• 72 49
• (491/2)2 49
• Thus 491/2 7
• Also 7
• Therefore 491/2
• 491/2 can be read as the square root of 49

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Definition of Fractional Exponents

• If a gt 0 and n is a natural number
• then a1/n is the positive real number
• such that (a1/n)n a.
• am/n n ?am (n ?a)m
• If a 0, then a1/n 0

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Examples
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Simplify use absolute value when necessary

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Simplify, write answers without negative exponents
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Simplify