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Negative and Zero Exponents Math Study Sheet, Study notes of Mathematics

Mathematics

Negative and Zero Exponents Math Study Sheet

Typology: Study notes

2019/2020

Uploaded on 11/10/2021

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3.10 Negative and Zero Exponents

Zero Exponents

Expressions

Expand and Simplify

Exponent Laws

35

3×3×3×3×3

3×3×3×3×3 =243

243 = 1

35−5 = 30= 1

43

4×4×4

4×4×4 =64

64 = 1

43−3 = 40= 1

(−3)4

(−3)×(−3)×(−3)×(−3)

(−3)×(−3)×(−3)×(−3) =81

81 =

(− 3)4−4 = (− 3)0= 1

(−2)2

(−2)×(−2)

(−2)×(−2) =4

4= 1

(− 2)2−2 = (− 2)0= 1

Negative Exponents

Expressions

Expand and Simplify

Exponent Laws

32

35

3×3

3×3×3×3×3 =1

3×3×3 =1

27

32−5 = 3−3 =3−3

1=1

33=

41

43

4

4×4×4 =1

4×4 =1

16

41−3 = 4−2 =1

42=1

16

(−3)4

(−3)7

(−3)×(−3)×(−3)×(−3)

(−3)×(−3)×(−3)×(−3)×(−3)×(−3)×(−3)

=1

(−3)×(−3)×(−3) =1

−27

(− 3)4−7 = (− 3)−3

=1

(−3)3=1

−27

(−2)3

(−2)5

(−2)×(−2)×(−2)

(−2)×(−2)×(−2)×(−2)×(−2)

=1

(−2)(−2) =1

4

(− 2)3−5 = (− 2)−2

=1

(−2)2=1

4

**DO NOT WANT NEGATIVE EXPONENTS IN YOUR FINAL ANSWER**

Note: the whole term does not undergo a sign change. ONLY EXPONENT’S SIGN CHANGES.

Zero Exponents: 1

𝑎𝑛𝑦𝑡ℎ𝑖𝑛𝑔0=

Negative Exponents: 𝑎−1 =1

𝑎1

(𝑎

𝑏)−1 =1

(𝑎

𝑏)1= 1 × ( 𝑏

𝑎)1

Shortcut: flip the fraction and change the exponent’s sign

1

Partial preview of the text

Download Negative and Zero Exponents Math Study Sheet and more Study notes Mathematics in PDF only on Docsity!

3.10 Negative and Zero Exponents

Zero Exponents Expressions Expand and Simplify Exponent Laws 35 35

3×3×3×3×

3×3×3×3×3 =^

243 = 1^3

= 3

= 1

43 43

4×4×

4×4×4 =^

64 = 1^

4

= 4

= 1

(−3)^4 (−3)^4

(−3)×(−3)×(−3)×(−3)

(−3)×(−3)×(−3)×(−3) =^

81 =

(− 3)

= (− 3)

= 1

(−2)^2 (−2)^2

(−2)×(−2)

(−2)×(−2) =^

4 = 1^

(− 2)

= (− 2)

= 1

Negative Exponents Expressions Expand and Simplify Exponent Laws 32 35

3×

3×3×3×3×3 =^

3×3×3 =^

3

= 3

=

1 =^

=

41 43

4 4×4×4 =^

1 4×4 =^

1 16

4

= 4

=

(−3)^4 (−3)^7

(−3)×(−3)×(−3)×(−3) (−3)×(−3)×(−3)×(−3)×(−3)×(−3)×(−3)

= (^) (−3)×(−3)×(−3)^1 = (^) −27^1

(− 3)

4− = (− 3)

−

=

(−3)^3

=

(−2)^3 (−2)^5

(−2)×(−2)×(−2) (−2)×(−2)×(−2)×(−2)×(−2)

= 1 (−2)(−2) =^

1 4

(− 2) 3− = (− 2) −

=

(−2)^2

=

****DO NOT WANT NEGATIVE EXPONENTS IN YOUR FINAL ANSWER** Note: the whole term does not undergo a sign change. ONLY EXPONENT’S SIGN CHANGES.**

Zero Exponents: 𝑎𝑛𝑦𝑡ℎ𝑖𝑛𝑔 1

0 = (^) Negative Exponents: 𝑎−1^ = 1 𝑎 1

(

𝑎 𝑏 )

−

1 ( 𝑎𝑏 )

1 = 1 × (^

𝑏 𝑎 )

1

Shortcut: flip the fraction and change the exponent’s sign

Ex: Simplify using positive exponents. Then, evaluate (get a final answer with no exponent).

a) 5

−

51

= 15 b) 8

−

82

= 641 c) 11

0

d) (− 2)

−

(−2)^3

= −8^1 e) 2

−

= ( 32 )^2 = 3

2 22

= f)^0 →^ undefined

−

03

Product Rule (When multiplying powers that have the same base ⇒ add the exponents)

𝑎

𝑚 × 𝑎

𝑛 = 𝑎

𝑚+𝑛

Quotient Rule (When dividing powers that have the same base ⇒ subtract the exponents)

𝑚

÷ 𝑎

𝑛

𝑎𝑚 𝑎𝑛^

𝑚−𝑛

Power of a Power Rule (A power raised to another power ⇒multiply the exponents )

𝑚

𝑛

𝑚×𝑛

Ex: Apply exponent rules to simplify. Make sure all exponents are positive.

a) 𝑥

2

−

2+(−5)

−

= b) (𝑚^2 𝑛−4)

−

= 𝑚

2·(−3) 𝑛

−4·(−3)

= 𝑚

− 𝑛

12

6

c) 𝑦^5 𝑦^12

5−

−

1 𝑦^7

d) (− 2𝑎^3 𝑏)(4𝑎^2 𝑏^3 )

−

= (− 2𝑎^3 𝑏) · (4−2𝑎2×(−2)𝑏3×(−2)) ← Power of Power Rule first

3

1 16𝑎^4 𝑏^6

−2𝑎

3 𝑏 16𝑎

4 𝑏

6

3

4

6

−1 × 𝑎3−4^ × 𝑏1− 8

−

5

OR

(− 2𝑎 3 𝑏)(4𝑎 2 𝑏 3 )

−

Negative and Zero Exponents Math Study Sheet, Study notes of Mathematics

Related documents

Partial preview of the text

Download Negative and Zero Exponents Math Study Sheet and more Study notes Mathematics in PDF only on Docsity!

3.10 Negative and Zero Exponents

3×3×3×3×

4×4×

(−3)×(−3)×(−3)×(−3)

(−2)×(−2)

3×

(−3)^3

(−2)^2

−

a) 5

= 15 b) 8

= 641 c) 11

d) (− 2)

= −8^1 e) 2

= ( 32 )^2 = 3

= f)^0 →^ undefined

÷ 𝑎

a) 𝑥

= b) (𝑚^2 𝑛−4)

OR