Chapter 6.1
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This document contains examples of solving equations involving exponents and roots. It discusses the number of solutions when solving nth roots depending on if n is even or odd and if the radicand is positive, negative or zero. It also contains examples of solving equations with rational exponents and integer exponents.
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Chapter 6.1
- 1. Algebra 2
- 2. 32 = 9 102 = 100 2172 = 47089
- 3. 23 = 8 53 = 125 1713 = 5000211
- 4. For an integer n greater than 1, if b n = a, then The nth root of a is equal to b
- 6. Let n be an integer (n > 1), a is a real number and n is an even integer a < 0, no real nth roots a = 0, one real nth root a > 0, two real nth roots
- 7. Let n be an integer (n > 1), a is a real number and n is an odd integer a < 0, one real nth root a = 0, one real nth root a > 0, one real nth root
- 8. n = 5, a = -32 Answer, n is odd so there is 1 solution: n = 6, a = 1 Answer – n is even, a is positive so 1 solution:
- 9. Rational exponents don’t have to be in the form 1/n
- 10. 125 2/3 Answer : 125 2/3 = (125 1/3)2 = 52 = 25 8 -4/3 Answer: 1/16
- 11. Solve: 4x5 = 128 Solve: (x – 3)4 = 21 Solve: x6 – 34 = 181
- 12. Solve: 4x5 = 128 x = 2 Solve: (x – 3)4 = 21 x= Solve: x6 – 34 = 181 x=