Warm up 1-9-15
Simplify the following exponential terms:
3
4
3𝑥 6
3
1. 𝑦 ∙ 𝑦
4.
𝑦2
2. 𝑛
5.
2 5
3
3
4𝑥
𝑥9
3.
𝑥3
𝑥
4
6. 5𝑏 ∙ 𝑏
−7
UNIT 6 DAY 2: RATIONAL
EXPONENTS
Essential Question: What do you do when you have a
fraction as an exponent?
VOCABULARY
•
Radical: the square root symbol (
•
Radical Form: When a fraction exponent is
converted to a radical
•
Exponent Form: When a radical is converted
to a fraction exponent
)
THE NTH ROOT
An nth root is the inverse of the nth exponent. For example:
22 = 4
3
2 =8
4
2 = 16
5
2 = 32
6
2 = 64
so….
so….
so….
so….
so….
4
3
8
4
16
5
32
6
64
=2
=2
=2
=2
=2
…. and so on!
HOW CAN WE WRITE ROOTS AS
EXPONENTS…?
Let’s solve the following equation for x to see what a square
root would look like as an exponent:
(
3 )2 = ( 3x )2
31
=
32x
1
=
2x
1/2
=
x
Conclusion:
3
=
31/2
The denominator always becomes the root!
EXAMPLE 1: CONVERT FROM RADICAL FORM TO
EXPONENT FORM.
3
31/2
4
7
5
51/4
2
21/7
EXAMPLE 2: CONVERT FROM EXPONENT FORM
TO RADICAL FORM, THEN SIMPLIFY.
1251/3
3
1
125
5
811/4
641/6 + 251/2
4
6
811
3
1
64
+
2+5
7
1
25
EXAMPLE 3: CONVERT FROM RADICAL FORM TO
EXPONENT FORM.
35
35/2
4
7
53
53/4
22
22/7
EXAMPLE 4: CONVERT FROM EXPONENT FORM
TO RADICAL FORM, THEN SIMPLIFY.
163/4
4
4
3
16
4,096
8
12/5
5
5
274/3
3
2
1
1
1
3
4
27
531,441
81
EXAMPLE 5: THE APPROXIMATE NUMBER OF CALORIES (C) THAT AN
ANIMAL NEEDS EACH DAY IS GIVEN BY C = 72M3/4, WHERE M IS THE
ANIMAL’S MASS IN KILOGRAMS. FIND THE NUMBER OF CALORIES
THAT A 16KG DOG NEEDS EACH DAY.
C = 72M3/4
C = 72(16)3/4
C = 72 •
4
163
4
C = 72 • 4,096
C = 72 • 8
C = 576 CALORIES ARE NEEDED PER DAY
EXAMPLE 6: SIMPLIFY EACH EXPRESSION USING
RADICAL AND EXPONENT RULES.
3
x9y3
3
2
1/2
4
(x y )
y3
(x9y3)1/3
(x8y4/2)(y3)1/3
x9/3y3/3
(x8y2)(y3/3)
x3y1
(x8y2)(y1)
x8y3
SUMMARY
Essential Question: What do you do when you have a
fraction as an exponent?
Take 1 minute to write 2 sentences answering the essential
question.