W10D1 Exponents
Warm Up
1. Simplify 52
2. Simplify 23
3. Simplify x · x · x
4. Simplify 3x + 2x2 + x + 6x2
Lesson 22 Exponent Properties
Multiply and Divide
When in doubt, expand it out. When terms are multiplied add the exponents. When terms are divided subtract the exponents.
Follow the standard arithmetic rules for coefficients.
EX 1:
(3xy)(−2x)(y 2 )
EX 2:
20x3 y 10
8x8 y 7
−6x2 y 3
5y 3
2x5
Power to Power When in doubt, expand it out. When a power is raised to another power, multiply the exponents.
EX 3:
10x5 y 9
6x12 y 3
5
55 y 30
35 x35
Zero and Negative Exponent
5
=1
5
x3
= x3−3 = x0
x3
x0 = 1 Anything to the 0 exponent is 1
EX 4:
Simplify 4x0 y 3 = 4y 3 vs 4(xy 3 )0 = 4
x2
= x2−6 = x−4
x6
x3
x·x·x
1
Expand it out: 9 =
= 6 = x−6
x
x·x·x·x·x·x·x·x·x
x
EX 5:
Subtracting exponents:
Always write final answers with only positive exponents.
When you have a negative exponent it will ”move” from the numerator to the denominator or from the denominator to the
numerator.
EX 6:
EX 7:
6x2 y 3
3y 2
=
not 3y 2 x−5
2x10 y
4x5
x−5 y 3
y6
Simplify 6 −3 = 11
2x y
2x
Simplify
Practice Problems
1. (2ab−3 )−2 (2a−1 b)−4
2. (xy −1 · 2x−4 y −3 )2
4
2mn4 2m3
3.
(7n3 )2
(2x2 y 2 )3 · x2 y −1 · 2x2 y
4.
(2x3 y −2 )3
(x−4 y 3 )−4 · 2x−3 y 0
5.
2y −4
Answers
a2 b 2
26
4
2. 8 6
y x
28 m16
3. 8 8
7n
1.
4. 2xy 12
x13
5. 8
y
Extra Practice Work
6. (4xy 5 )(2x2 y 3 )
8x3 y 8
7. 3x2 + 5x2
8x2
8.
4x3 y 8
x5 y
4y 7
x2
9.
9x10 y 3
3x5 y 7
3x5
y4
10. (6x2 )(5x3 )
30x5
11. 7x5 − 2x5
5x5
12. (−4a2 b3 )(6a4 b2 )
−24a6 b5
13. 8y 3 + 2y 4
8y 3 + 2y 4
14.
y7
y2
y5
15.
x5 y 8
xy 3
x4 y 5
16.
x4 y 3
xy 9
x3
y6
17.
x6 y 2
xy 2
x5
Power to Power When in doubt, expand it out. When a power is raised to another power, multiply the
exponents.
(33 )4 = (3 · 3 · 3)4 = (3 · 3 · 3)(3 · 3 · 3)(3 · 3 · 3)(3 · 3 · 3)
312
(3x2 )(3x2 )(3x2 ) = 33 x6 = 27x6
(3x2 )3
(2g 5 h3 )(2g 5 h3 )(2g 5 h3 )(2g 5 h3 )
24 g 20 h12
1. (−3a6 b5 )2
2
x5
y
2x6 y 3
x4 y 7
2.
3.
9x12 y 10
x10
y2
4
16x8
y 20
2
−5x3 y
xy 4
6 5 3
3x y
12xy 8
25x4
y6
4.
5.
x15
81y 9
6. (4x2 y 5 )3
7.
x3 y 2
y4
64x6 y 15
2
x6
y4
(x5 y 2 )4
x20 y 8
(5x3 y 2 )(5x3 y 2 )
25x6 y 4 = (5x3 y 2 )2
(3y 4 )2
9y 6
(5x3 y 6 )3
125x9 y 19
Zero and Negative Exponent
5
x3
EX 1:
=1
= x3−3 = x0
5
x3
x0 = 1 Anything to the 0 exponent is 1
EX 2:
Simplify 4x0 y 3 = 4y 3 vs 4(xy 3 )0 = 4
EX 3:
Subtracting exponents:
x2
= x2−6 = x−4
x6
Expand it out:
x3
1
x·x·x
= 6 = x−6
=
9
x
x·x·x·x·x·x·x·x·x
x
Always write final answers with only positive exponents.
When you have a negative exponent it will ”move” from the numerator to the denominator or from the
denominator to the numerator.
EX 4:
EX 5:
3y 2
6x2 y 3
Simplify 10 = 5 not 3y 2 x−5
2x y
4x
x−5 y 3
y6
Simplify 6 −3 = 11
2x y
2x
6. 4x−2 y 3
4y 3
x2
7. 7x4 y −5 z −1
7x4
y5z
8. 6(x2 y)−3
9.
10.
3x−4 y 2
5z 3
4a7
10c−8 b2
Exit Pass 2
9x5 y 4
1. Simplify
x3 z 8
2. Simplify (5x−4 y)2 (x6 y −2 )
3. What does m equal? (x3 y 2 )4 = xm · x5 · y 8
81x4 y 8
1. 16
z
25y 4
2.
x2
3. (xm y 4 )2
9x2 y 3
81
1. Simplify ( 6 5 )2 = 8 4
xy
xy
9y 6
2. Simplify (9x−6 y)(x2 y −5 ) = 7
x
6
x6 y 3
3y 2
5x4 z 3
2a7 c8
5b2