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##### Warm Up

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**Warm Up**• Write down the best thing you did over the holiday break**Algebra 3Chapter 7: POWERS, ROOTS, and RADICALSLesson 1: nth**roots and rational exponents**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**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**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.**Directions (Writing Roots)**• Plug the numbers into the formula**I DO (Writing Roots)**• 1. n = 3 a = 8 • 2. n = 5 a = 7 • 3. n = 2 a = 6 • 4. n = 9 a = 12**WE DO (Writing Roots)**• 1. n = 6 a = 98 • 2. n = 7 a = 37 • 3. n = 3 a = 7 • 4. n = 13 a = 4**YOU DO (Writing Roots)**• 1. n = 5 a = 86 • 2. n = 71 a = 73 • 3. n = 21 a = 64 • 4. n = 13 a = 1296**Directions (Rewriting Problems)**• Use the formula to rewrite**I DO (Rewriting Problems)**• 1. • 2. • 3. • 4.**WE DO (Rewriting Problems)**• 1. • 2. • 3. • 4.**YOU DO (Rewriting Problems)**• 1. • 2. • 3. • 4.**Review**• Today you learned how to rewrite radical expressions**Homework**• Worksheet • 7.1A (1 – 24)**Warm Up**Rewrite • 1. • 2.**Algebra 3Chapter 7: POWERS, ROOTS, and RADICALSLesson 1: nth**roots and rational exponents**TODAY**• We will evaluate rationals by hand and in the calculator.**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**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**I DO (Hand)**• Evaluate the expression by hand 1. 2. 3. 4.**WE DO (Hand)**• Evaluate the expression by hand 1. 2. 3. 4.**YOU DO (Hand)**• Evaluate the expression by hand 1. 2. 3. 4.**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**I DO (Calculator)**• Evaluate using the calculator and then round to 2 decimals. • 1. • 2. • 3. • 4.**WE DO (Calculator)**• Evaluate using the calculator and then round to 2 decimals. • 1. • 2. • 3. • 4.**YOU DO (Calculator)**• Evaluate using the calculator and then round to 2 decimals. • 1. • 2. • 3. • 4.**Review**• What did you learn today?**Homework**• Worksheet • 7.1 (25 – 45)