Lesson36

# Lesson36 - Lesson 36 Section 7.2 1 2 What is a value for 9...

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1 Lesson 36 Section 7.2 What is a value for 2 1 9 ? Consider This. 9 9 9 9 9 1 2 1 2 1 2 1 2 1 = = = × + using the product rule of exponents. Now, Think! What other number times itself equals 9? 9 3 3 = × Since both products equal 9, we can conclude that 3 9 2 1 = . Conclusion: A rational exponent is the same as a root! Definition of a rational (fractional) exponent: n n a a = 1 Evaluate or write an equivalent root for each. Simplify, if possible. 1. = 2 1 16 2. = 3 1 x 3. = - 5 1 ) 32 ( 4. = 4 1 ) 4 ( c Write an equivalent expression using exponential notation. 5. = 4 5 6. = 3 2 ab 7. = n Expanded Definition of a rational (fractional) exponent: ( ) m n n m n m a a a or = Proof: ( ) ( ) 1 1 m m m n n n m m m n n n a a a a a a = = = =

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2 Notice: The exponent m can be inside the radical (in the radicand) or outside of the radical. The order does not matter. You can raise to the m power first and then take the n th root. Or you can take the n th root and then raise to the
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Lesson36 - Lesson 36 Section 7.2 1 2 What is a value for 9...

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