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Warm Up

Warm Up. Write down the best thing you did over the holiday break. Algebra 3 Chapter 7: POWERS, ROOTS, and RADICALS Lesson 1: n th roots and rational exponents. VOCAB. Index – is the number of the radical n th root of a – is All powers can be transformed into radical expressions

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Warm Up

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  1. Warm Up • Write down the best thing you did over the holiday break

  2. Algebra 3Chapter 7: POWERS, ROOTS, and RADICALSLesson 1: nth roots and rational exponents

  3. VOCAB • Index – is the number of the radical • nth root of a – is • All powers can be transformed into radical expressions • Examples we know so you solve it by doing the opposite which is a square root • If the power is bigger than 2 you do an nth root which means

  4. Rules • N is odd then a has one root • N is even and a > 0 then a has 2 real roots • N is even and a = 0 then a has 1 real root and it is 0 • N is even and a < 0 then a has 0 real roots but 2 imaginary roots

  5. TODAY • Today we will be learning how to write powers as exponential equations. In order to solve them you have to understand what they mean.

  6. Directions (Writing Roots) • Plug the numbers into the formula

  7. I DO (Writing Roots) • 1. n = 3 a = 8 • 2. n = 5 a = 7 • 3. n = 2 a = 6 • 4. n = 9 a = 12

  8. WE DO (Writing Roots) • 1. n = 6 a = 98 • 2. n = 7 a = 37 • 3. n = 3 a = 7 • 4. n = 13 a = 4

  9. YOU DO (Writing Roots) • 1. n = 5 a = 86 • 2. n = 71 a = 73 • 3. n = 21 a = 64 • 4. n = 13 a = 1296

  10. Directions (Rewriting Problems) • Use the formula to rewrite

  11. I DO (Rewriting Problems) • 1. • 2. • 3. • 4.

  12. WE DO (Rewriting Problems) • 1. • 2. • 3. • 4.

  13. YOU DO (Rewriting Problems) • 1. • 2. • 3. • 4.

  14. Review • Today you learned how to rewrite radical expressions

  15. Homework • Worksheet • 7.1A (1 – 24)

  16. Warm Up Rewrite • 1. • 2.

  17. Algebra 3Chapter 7: POWERS, ROOTS, and RADICALSLesson 1: nth roots and rational exponents

  18. TODAY • We will evaluate rationals by hand and in the calculator.

  19. Directions (HAND) • Think small to big. ROOT1 2 3 4 5 6 • 1 1 1 1 1 1 • 2 4 8 16 32 64 • 3 9 27 81 243 729 • 4 16 64 256 1024 4096 • 5 25 125 625 3125 15625 • 6 36 216 1296 7776 46656 • 7 49 343 2401 16807 117649

  20. Special Directions • When you have a negative exponent • Change the exponent to a positive • Flip the numerator and denominator • AKA reciprocal • EVEN POWERS NEED ± • EXCEPT when there is a negative out front

  21. I DO (Hand) • Evaluate the expression by hand 1. 2. 3. 4.

  22. WE DO (Hand) • Evaluate the expression by hand 1. 2. 3. 4.

  23. YOU DO (Hand) • Evaluate the expression by hand 1. 2. 3. 4.

  24. Directions (Calculator) • Write the problem in exponent form • Type in the calculator • Remember the ^ is for big powers • Remember you need parenthesis for negatives and fractions • ROUND to 2 decimals

  25. I DO (Calculator) • Evaluate using the calculator and then round to 2 decimals. • 1. • 2. • 3. • 4.

  26. WE DO (Calculator) • Evaluate using the calculator and then round to 2 decimals. • 1. • 2. • 3. • 4.

  27. YOU DO (Calculator) • Evaluate using the calculator and then round to 2 decimals. • 1. • 2. • 3. • 4.

  28. Review • What did you learn today?

  29. Homework • Worksheet • 7.1 (25 – 45)

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