Warm Up

Warm Up

•Write down the best thing you did over theholiday break

Algebra 3Chapter 7: POWERS, ROOTS, andRADICALSLesson 1: nth roots and rationalexponents

VOCAB

Index – is the number of the radical
nth root of a – is 𝑛 𝑎

All powers can be transformed into radical expressions
Examples we know 2 2 =4 so you solve it by doing the opposite which is a square root 4 =2
If the power is bigger than 2 you do an nth root 2 3 =8 which means 3 8 =2

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 andit is 0

•N is even and a < 0 then a has 0 real roots but2 imaginary roots

TODAY

•Today we will be learning how to write powersas exponential equations. In order to solvethem you have to understand what theymean.

Directions (Writing Roots)

•Plug the numbers into the formula

I DO (Writing Roots)

•1. n = 3a = 8

•2. n = 5a = 7

•3. n = 2a = 6

•4. n = 9a = 12

WE DO (Writing Roots)

•1. n = 6a = 98

•2. n = 7a = 37

•3. n = 3a = 7

•4. n = 13a = 4

YOU DO (Writing Roots)

•1. n = 5a = 86

•2. n = 71a = 73

•3. n = 21a = 64

•4. n = 13a = 1296

Directions (Rewriting Problems)

•Use the formula to rewrite

I DO (Rewriting Problems)

1. 3 −125 =−5
2. 16 1 4 =2
3. 5 7 2
4. 3 3 4

WE DO (Rewriting Problems)

1. − 9 1124
2. 6 1 3
3. 6 9 5
4. 10 3 7

YOU DO (Rewriting Problems)

1. 3 11
2. 2 1 2
3. ( 3 27 ) 4
4. 9 2 7

Review

•Today you learned how to rewrite radicalexpressions

Homework

•Worksheet

–7.1A (1 – 24)

Warm Up

Rewrite
1. 5 34 3
2. 19 4 9

Algebra 3Chapter 7: POWERS, ROOTS, andRADICALSLesson 1: nth roots and rationalexponents

TODAY

•We will evaluate rationals by hand and in thecalculator.

Directions (HAND)

•Think small to big.

ROOT 123456

•111111

•2 48163264

•392781243729

•4166425610244096

•525125625312515625

•6362161296777646656

•749343240116807117649

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. 3 64
2. 3 −1000
3. − 6 64
4. 4 − 1 2

WE DO (Hand)

Evaluate the expression by hand
1. 1 1 3
2. −(256 1 4 )
3. ( 4 16) 2
4. ( 3 −27) −4

YOU DO (Hand)

Evaluate the expression by hand
1. ( 6 0 ) 3
2. −(16 − 3 2 )
3. 32 4 5
4. (−125) − 2 3

Directions (Calculator)

•Write the problem in exponent form

•Type in the calculator

–Remember the ^ is for big powers

–Remember you need parenthesis for negativesand fractions

•ROUND to 2 decimals

I DO (Calculator)

Evaluate using the calculator and then round to 2 decimals.
1. 5 −16807
2. 9 1124
3. 8 65536
4. 4 1 10

WE DO (Calculator)

Evaluate using the calculator and then round to 2 decimals.
1. 10 − 1 4
2. − (1331 1 3 )
3. ( 3 112 ) −4
4. ( 7 −280 ) 3

YOU DO (Calculator)

Evaluate using the calculator and then round to 2 decimals.
1. ( 6 6 ) 2
2. (−190) − 4 5
3. 26 − 3 4
4. 522 2 7

Review

•What did you learn today?

Homework

•Worksheet

–7.1 (25 – 45)