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## Chapter 7 Powers, Roots and Radicals

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**Chapter 7Powers, Roots and Radicals**• We’ll be studying sections 7.1 – 7.6 • A lot of new material • Homework is online • I’ll check HW daily • Randomly collect a HW weekly • Expect a quiz on Fridays • Chapter test around February 21**nth Roots and Rational Exponents**Section 7.1 p401**What we’ll talk about today**• What is an nth root? • Radical and exponent notation • Real number roots • Rational exponents • Roots and your calculator • Solving an equation using nth roots**nth roots**• Recall the definition of a square root • A number r is a square root of a number s if r 2 = s. • This means that r x r = s**Section 5.3 Review**Radical Sign Radicand Radical expression**Other roots**• Extending the definition of square roots, if bn= a, then b is the nth root of a. • An nth root can be written as n√a, where n is the index of the radical.**Rational Exponents**• If √a = ak, then what is k? From the definition of square root: √a √a = a akxak=a1, so ak+k = a1 Since the bases are the same 2k = 1, k = ½ What does this mean? The rational exponent of ½ is the same as the square root.**Rational exponents**Let a1/n be an nth root of a and let m be a positive integer. • am/n = (a1/n)m = (n√a)m**Using a calculator**• Option 1: Use the rational exponent notation. Pay attention to parentheses and the order of operations! 102/5 would be entered as 10^(2/5) ≈2.512**Evaluate to the nearest hundredth.**≈ 43.22 ≈ 0.12**Evaluate to the nearest hundredth.**≈ 43.22 ≈ 0.12**Using a calculator**• Option 2: Use the radical notation. Use parentheses! would be entered as 6 (index) MATH 5:x√ (530)^7**Without a calculator, find the indicated nth root of a.**Use prime factorization if you are stuck. • n = 5, a = -32 • n = 4, a = -81 no real solution • n = 4, a = 16**Solving equations using nth roots**• How do you think we’ll solve these equations: