Exponents INTEGRATED MATHEMATICS. Multiplying Using Exponents 8 3 8 2 means 5 2 5 4 means What did...
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Transcript of Exponents INTEGRATED MATHEMATICS. Multiplying Using Exponents 8 3 8 2 means 5 2 5 4 means What did...
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