Warm Up:

5.1 Notes: nth Roots and Rational

Exponents

What is a radical? A radical is a symbol for finding the root of a

number. This could be a square root, cube root, 4th root, 5th root, etc.

Even roots: = 2 real roots, one positive & one

negative = 0 = no real roots, an “i” would need to be

used.

a0a

Odd roots: = one real root that is positive,

because “a” is positive = 0 = one real root that is negative,

because “a” is negative EX: Find each root – 1) 2) 3) 4)

3 a3 03 a

4 16 3 27 6 64 5 32

Evaluating Expressions with Rational Exponents (No Calculator)

Evaluate …..How? Well, we split the fraction up.

Change this to …the numerator goes on the outside, the denominator stays on the inside. Evaluate the root (the fraction) first, then take the exponent of that answer.

23

163

21

16

Evaluate: A) B) C)

53

32

34

64 45

16

Rational Exponents Question: Can we type in to the

calculator? What about ? How can we find the answers without

having to do factor trees? ANSWER: Rational exponents Rational exponents: exponent(power) root So, = =

3 2167 2)536(

3 216 7 2)536(

Now what? Now, we can type these into our

calculators: 216 ^ (1 ÷ 3) = ( - 536 ) ^ (2 ÷ 7) =

You try:52

6 32

64

54 )16( 23 30

What do we do to solve equations with exponents?

We use SADMEP to solve them, just that we will need to remember to use the reciprocal power when doing opposite operations!

If your original exponent was EVEN you will have TWO answers, a positive and a negative one!

Round all answers to the hundredths place.

Examples: A) x4 = 60 B) x1/2 = 12 C)

2(x + 2)3 = 54

D) (x – 6)2/5 = 37 E) x3 + 23 = 2153

F) 2x-1/2 + 6 = 16

31

HW:

P. 241 – 242 #11 – 31 odd, 35 – 43 odd