Unit 3: Part 1 Exponents
Name: ___________________________
3-1 Notes
-4a
Base –
Exponent –
3
Coefficient –
Exponents are used when we _____________ a number or variable
repeatedly.
Examples: Write each expression using exponents.
1.
5∙5∙5
3.
d∙d∙d∙d∙d∙d
2.
p
4.
(6)(6)(-7)(-7)(-7)(-7)(-7)
* Put negative bases in parentheses.
Examples: Write each power as a multiplication expression.
5.
64
6.
(-h)3
7.
7a3b2
8.
(7a)3
Keystone Questions:
Ex 1. What is the value of -4g3h2 when g = 2 and h = 4?
Ex 2. What is the value of 2|𝑥 2 + 1| when x = -8?
Unit 3: Part 1 Exponents
Ex 3. Which of the following inequalities is true when x = 2?
A. 2x3 + 5 > 3x2 + 10
B. 4x2 > 4x2
C. 2x2 > (x + 1)2
D. x4 < 3x3
3-1 Practice
Write each expression using exponents.
1) 6 ∙ 6 ∙ 6 ∙ 6 ∙ 6
2) 8 x 8
3) x ∙ x
4) (-4)(-4)(-4)
5) a ∙ a ∙ a ∙ b ∙ b
6) 4 ∙ 4 ∙ x ∙ x ∙ y
Write each power as a multiplication expression.
7) 93
8) (-5)5
9) 43 ∙ 23
10) m5n3
11) (2x)2
12) 3x2y4
Evaluate each expression if x = 2 and y = -2.
13) x2
14) y2
15) x3
16) y3
17) 2(x + 3)2
18) 4|𝑦|
Unit 3: Part 1 Exponents
3-1 Practice Continued
Simplify each expression. Show each step.
19) 4(62 - 4∙4)2
21)
52 +15
5+3
20) 8|23 − 32 |
22) 4∙32 – 20
Unit 3: Part 1 Exponents
3-2 Notes
Zero Exponent: Anything raised to the power of zero is _____________.
1) 40=
2) x0 =
3) (4xy)0 =
4) (-216)0 =
Negative Exponent: A negative exponent is the ______________ of a positive
exponent. Since we use positive exponents when we multiply, a negative
exponent means to ____________________.
1) 8-1
2) 2-4
3) x-2
4) 2-2
Main Idea. To evaluate a negative exponent, take the __________________
1 −2
5) ( )
2
1 −3
6) ( )
3
Unit 3: Part 1 Exponents
“Can’t I just use my calculator?!”
Yes.. If you know how to use your calculator correctly.
Evaluate each expression using just your calculator. Give each answer as a
fraction.
1 2
1. -24
4.
2. 4( )
3. 4-1
5. 4(2√4)-2
6. ( )
2
2+7
2−5
1 −2
2
Practice: Set up each problem. Then evaluate each expression for
x = 5, y = -1 and z = 4.
1) y 4 
2) 3x3 
3) 2y 2 
4) z 2 
5)  yz  
6)  yx  
7) x 2 z 2 
8) y x 
2
3
Unit 3: Part 1 Exponents
3-3 Notes: Multiplying Monomials
Write each power as a multiplication expression.
1.
Multiply x3 ∙ x4
2.
Multiply c2 ∙ c
Product of Powers Pattern:
When you _________________ powers with the same base you
__________________ the exponents.
Remember:
1. If you do not see an exponent for a variable there is really a _________ there.
2. Coefficients get _________________ by other coefficients.
Examples: Simplify each expression.
1.
(21c6)(c7)
2.
8x4 • 3x
3.
(2a4)(2a3b2)(-3ba2)
Unit 3: Part 1 Exponents
You Try!
Simplify
1. c4 • c7
2. a • a9
3. c4 • c3
4. c10 • 4c2
5. (-2c 3)(3c12)
6. g(g5)
7. (d2)(d3)(d4)
8. 3y2xy2
9. 4a6b • 2a3
10. p • 3p4
11. yx4 • 3x3y
12. 3m2 • 2m
13. (4a2)(3ba4)(3ab4)
14. x • x3
15. (3n)n2
16. 3k3 • 3k3
17. 2v3 • 4uv
18. (b3)b
Unit 3: Part 1 Exponents
3-4 Notes: Power Raised to a Power
Write each power as a multiplication expression.
1.
(x3)5
2.
(2c2)4
Power to a Power Pattern:
When you raise a power to a power you __________________ the exponents.
Remember: Coefficients must be _____________ to the ___________.
GET RID OF ANY EXPONENTS OUTSIDE OF PARENTHESES FIRST!
Examples: Simplify each expression.
1.
(2x4)3
2.
(-2t4)5
3.
(a4)(a7)
4.
(2p3)2
5.
(x4y5)2(-5xy)
6.
(3x2y3)(-2x3y4)2
7.
(-5mn)2(2mn4)2
8.
(-u)4
Unit 3: Part 1 Exponents
3-2 Practice
Simplify.
1) (3k)2
2) (3p2)2
3) (x3)2
4) (2n3)2
5) (r2)5
6) (2x2)2
7) (a4b2)2
8) (y2)4
9) (-3m)2
10) (3x4y4)4
11) (4m)4
12) (2yx3)4
13) (2v3)4v2
14) (-2a4)2 ∙ 2a4
15) -2x2 ∙ (2x2)4
16) (2x4)2
17) k4(2k4)4
18) (2a2)3
19) 2vu2 ∙ (v3)4
20) (y3)2 ∙ -2x3y3
21) (-u4)4 ∙ 2uv3
22) yx2 ∙ (yx4)3
23) a2b3 ∙ (2a2b4)4
24) (2x4y3)3 ∙ x2y4
Unit 3: Part 1 Exponents
3-5 Notes
Write each power as a multiplication expression.
1.
4c5
=
2c 2
6 x6 y
=
8x4 y3
2.
Rule: When dividing monomials:
 ___________ or ________________ the coefficients
 ________________ the exponents. If the result is a negative exponent
move the monomial to where the ____________________ exponent was.
 Get rid of any exponents ____________ of the parentheses first!
Examples:
1.
3.
8m 7 n 5
6mn 2
4𝑎8 𝑏3 𝑐 2
−28𝑎5 𝑏6 𝑐 3
2.
4.
34 a 2b3
32 a5b
16(𝑐 −2 𝑑−1 )−3
4𝑐 3 𝑑3
Unit 3: Part 1 Exponents
Recall: Zero Exponent: Anything raised to the zero power is _________.
Ex 1.
𝑥2
𝑥2
Ex 2.
(3𝑥)0
4
You Try!
1.
3.
3𝑥 5 𝑦2
9𝑥 2 𝑦 5
−10𝑎2 𝑦 5
2𝑎𝑏2
2.
4.
−9𝑥 8 𝑦 3
−3𝑥 3 𝑦 3
4𝑥𝑦 2
8𝑥 2 𝑦5
Unit 3: Part 1 Exponents
3-5a Notes:
Recall negative exponents.
1)
4-1
2)
n-1
Dealing with negative exponents:
If the negative exponent is in the numerator, move it to the
__________________.
If the negative exponents is in the denominator, move it to the
___________________.
Simplify each expression. Your answer should contain only positive exponents.
1.
3u 5v 2
=
4vu 3
2.
5 x 4 y 0
=
5x4
3.
16u 2 v
=
4u 4 v 4
4.
3x5 y 3
=
4 x 4 y 4
Unit 3: Part 1 Exponents
5.
3a 4b4
=
a 2b
6.
4x 4 y 4
=
x4
7.
5 p3

15 pm2 q 2
8.
11xy 3
=
22 x3 z 2
9.
5mp

5 pm4 n3
10.
5 x 4 y 5 z 5
=
2 x 2 y 3 z 3
11.
2 xz 4
=
4 x3 y 4 z 5
12.

5 p 4 q5r 0
=
5rq 5
13.
x 4 y 3 z 2

3zx 2 y 2
14.

2 a 3b 5 c 5
=
4a 2b 2
Unit 3: Part 1 Exponents
Unit 3: Part 1 Exponents