Honors Math 2 Name: Nth Roots and Rational Exponents Date:

```Honors Math 2 Name: Nth Roots and Rational Exponents Date: Warm Up Find each of the following without a calculator. !
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27 16 1 125 Here is our definition of square root. If π ≥ 0, the square root π is a real number s such that π  ≥ 0 and π  ! = π Using this as a guide, write a definition for the following: Cubed Root Fourth Root nth Root All the properties of square roots apply to πth roots. !
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π₯ β ! π¦ = !
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= !
−27 Rational Exponents !
What do fractional exponents mean? Start with 8 ! . Can you explain why !
8 ! = 2? (Hint: Think about your definition of nth root) !
Evaluate 8 ! !!
Evaluate 8 ! Definition !
For integers π and π with π &gt; 0, if π ! is a real number, then !
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π != π ! =
π !
Why does the definition include the restriction that π ! is a real number? For You to Do Evaluate the following expression: !
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a. 27 β 27 !
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b. ! !&quot; !
Homework: p. 30-&shy;β32 #1, 5, 6 p. 56 #2, 4, 9-&shy;β11, 13 !
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c. 16! ```