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Published byConstance Lewis Modified over 8 years ago

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Review: Laws of Exponents

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Questions Q: 4 0 =? A: 1 Q: 4 1 =? A: 4 Q: 4 1/2 =? A: Let’s square the number (4 1/2 ) 2 =? (4 1/2 ) 2 = 4 1 = 4 Recall: b is called a square root of the number a if b 2 = a. 4 1/2 is a square root of the number 4 Or

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Definition of Rational Exponent Q: 8 1/3 =? A: Let’s cube the number (8 1/3 ) 3 =? (8 1/3 ) 3 = 8 1 = 8 So, we have In general, for any positive integer n,

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Examples Evaluate the following expressions

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Examples Simplify the following expressions

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Question Which way do you prefer?

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Definition of Rational Exponent The numerator m will the exponent The denominator n will be the index of the radical 25 3/2 = 3 2

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Examples 100 7/2 = (-27) 2/3 = 3/2 7 2 2 3 3 2

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Examples Simplify the following expressions

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Examples Simplify the following expressions

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