4.1 Power Rules€¦2.2 Adding, Subtracting and Multiplying Polynomials Author: Maia Clark Created...
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4.1 Power Rules
Transcript of 4.1 Power Rules€¦2.2 Adding, Subtracting and Multiplying Polynomials Author: Maia Clark Created...
4.1 Power Rules
Objectives•Simplify exponential expressions using power rules
•Evaluate expressions with negative or zero exponents
•Convert between scientific and decimal notation
•Use scientific notation to multiply and divide
POWER RULESThe same way that multiplication is shorthand for repeated addition, exponents are shorthand for repeated multiplication.
10 + 10 + 10 + 10 + 10 = 5(10)
vs
10 ∗ 10 ∗ 10 ∗ 10 ∗ 10 = 105
POWER RULES
𝑎𝑛𝑎 is called the base
𝑛 is called the exponent or power
ALL POWER RULES REQUIRE COMMON BASES
POWER RULES – MULTIPLY/DIVIDEWhen multiplying/dividing common bases, add/subtract the exponents.
𝑎𝑚 ∗ 𝑎𝑛 = 𝑎𝑚+𝑛
𝑎𝑚
𝑎𝑛= 𝑎𝑚−𝑛
POWER RULES – MULTIPLY/DIVIDE
𝑎𝑚 ∗ 𝑎𝑛 = 𝑎𝑚+𝑛 𝑎𝑚
𝑎𝑛= 𝑎𝑚−𝑛
1. 32 ∗ 33 = 3. 64
6=
2. 2𝑧2 ∗ 5𝑧4 = 4. 25𝑚8
15𝑚3 =
POWER RULES – ZERO Any number or variable with a zero exponent equals 1.
𝑎𝑚
𝑎𝑚= 𝑎𝑚−𝑚 = 𝑎0 = 1
5. 50 =
6. 18𝑥0 =
POWER RULES – NEGATIVEExponents are shorthand for repeated multiplication, meaning negative exponents are shorthand for repeated division.
𝑎−𝑛 =1
𝑎𝑛or
1
𝑎−𝑛= 𝑎𝑛
POWER RULES - NEGATIVE
𝑎−𝑛 =1
𝑎𝑛or
1
𝑎−𝑛= 𝑎𝑛
7. 5𝑏−4 =
8. 5
3𝑧−3 ∗ −
9𝑧4
20=
POWER RULES – POWER TO A POWERWhen multiple exponents appear, multiply the exponents.
𝑎𝑚 𝑛 = 𝑎𝑚𝑛
9. 𝑥2 4 =
10. 72 0 =
POWER RULES – PRODUCT/QUOTIENTWhen multiplying/dividing bases, the exponent can be distributed to all of the grouped bases.
𝑎𝑏 𝑛 = 𝑎𝑛𝑏𝑛
𝑎
𝑏
𝑛=
𝑎𝑛
𝑏𝑛
POWER RULES – PRODUCT/QUOTIENT
𝑎𝑏 𝑛 = 𝑎𝑛𝑏𝑛𝑎
𝑏
𝑛=
𝑎𝑛
𝑏𝑛
11. 2𝑎 4 = 13. 𝑧
3
3
12. −4𝑏3 −2 = 14. 5𝑏3
𝑐2
−2
=
SCIENTIFIC NOTATIONA number written in scientific notation has the form
𝑎 × 10𝑛
where 1 ≤ 𝑎 < 10 (single digit) and 𝑛 is an integer
SCIENTIFIC NOTATIONWrite the following in scientific notation.
15. 238,400
16. 0.071
SCIENTIFIC NOTATIONWrite the following in decimal notation.
17. −2.8 × 104
18. 1.49 × 10−5
SCIENTIFIC NOTATIONScientific notation follows normal power rules.
Simplify.
19. (3 × 102)(2 × 104)
20. (3.2 × 10−3)(4.8 × 10−4)
SCIENTIFIC NOTATIONScientific notation follows normal power rules.
Simplify.
21. 2.8×109
1.4×104
22. 3.6×103
7.2×10−1
