ExponentsINTEGRATED MATHEMATICS

Multiplying Using Exponents

83 • 82 means52 • 54 means

What did we do with the exponents?

Multiplying Using Exponents

Rule:

*When the bases are the same, add the exponents.

Example 1

Example 2

𝑎5∙𝑎3

Example 3

𝑦 3∙ 𝑦 2∙ 𝑦5

Example 4

(𝑚𝑛2)(𝑚4𝑛6)

Example 5(−7 𝑥2 𝑦5)(4 𝑥 𝑦 3)

Example 6

(4𝑚2)(2𝑚2)(−𝑚)

Example 7

(−3𝑎)(4𝑎2)(−𝑎4)

Practice: 1.2 • 25

2.g2 • g3

3.6c • 3c2

4.5b5 • 3b4

5.22 • 26

6.9ng6 • 6n3g4

7.6b2h3 • 3bh6

8.6n3 • 3n4k2

9.s6 • s5 • s3

10.k6g2 • 6k4g5 • 3kg4

11.6z3 • 5z5 • 9z2

Raising a Power to a Power

Rule:

*Multiply the exponents

Example 8

(35)4

Example 9

(𝑦5)3

Example 10

(𝑎6)3

Example 11

(3 𝑦)2

Example 12

(4 𝑥3)2

Example 13

(5 𝑥3 𝑦5𝑧 2)4

Example 14

(7 𝑥9 𝑦6)0

Practice Problems1.

2.

3.

4.

5.

6.

7.

8.

9. 10. 11. 12. 13. 14. 15.

Dividing Using ExponentsRule:

*When the bases are the same, subtract the exponents.

Example 15

45

42

Example 16

𝑥6

𝑥2

Example 17

𝑝5𝑝7

𝑝2𝑝5

Example 18

𝑔5

𝑔5

Example 19

3𝑥4

6 𝑥2

Example 20

10𝑥5 𝑦4

5 𝑥3 𝑦 2

Negative Exponents

Rule:

* NEVER leave negative exponents in your answers!!

𝑎−𝑚=1

𝑎𝑚

Example 21

5𝑚− 3

Example 22

𝑎𝑏−1

Example 23

2𝑥12𝑥4 𝑦 6

Example 24

3𝑎2𝑏7

5𝑎5𝑏

Example 25

𝑝0

Example 26

3𝑣4𝑤6

24𝑣𝑤8

Example 27

4𝑐3

16𝑐3

Example 28

(52)6÷512

Example 29

(25)2÷ 28

Example 30

(39)3÷330

Example 31

43 𝑥 (42)−4

Example 32

113 𝑥11− 7

Example 33

515 𝑥5− 8