Chapter 6.1(a) Integer Exponents.notebook
January 09, 2017
Bellwork
1) What was the best part of Winter Break? The worst?
2) Solve:
Chapter 6.1(a) Integer Exponents a. 3x + 4 = 18
b. 2(x ­ 4) = 16
Discover and use the product rule and quotient rule for exponents.
3) Simplify:
a. 63
b. (­2)6
c. ­35
Dec 16­2:14 PM
Dec 16­2:21 PM
Properties of Exponents Foldable
Exponential Expressions: expressions that contain exponents.
Exponents
Base: Number being Multiplied
Exponents: How many times the base is used as a factor
Negatives
No Parenthesis ­ Negative goes straight to answer
Parenthesis ­ Negative goes with the problem (use it to solve)
3 Exponent
4
BASE
If you substitute a number for a variable use parenthesis.
4 4 4 = 64
Examples: (­5)4 = (­5)(­5)(­5)(­5) ­62 = ­(6 6) Any base raised example:
to the power of 41 = 4
______ is equal b1 = b
to _______.
(Note: Any number or variable without an exponent has an exponent of 1.)
Identity Property of Exponents
Any nonzero base Zero Exponent raised to the power Property
of ______ is equal to _______.
example:
50= 1
a0 = 1
(Note: 00 is undefined)
Dec 16­2:23 PM
Can you find a pattern or shortcut from writing it all the way out each time? 43 42 = (4 4 4)(4 4) = 45 Dec 16­2:29 PM
To ___________ powers with the Product Rule
same base, _____ the exponents. a4 a6 = (a a a a)(a a a a a a) = a10
example:
32 35 = 37
a7 a4 = a11
x3 x x4 = (x x x)(x)(x x x x) = x8
Dec 16­2:33 PM
Dec 16­2:33 PM
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Chapter 6.1(a) Integer Exponents.notebook
January 09, 2017
Which of the following is not true? Explain.
Use the product rule to simplify:
a. 32 35 31 = 32+5+1 = 38
3
2
3+2
a. 52 56
d. 22a3 2a5
b. x5 x9
e. x3y4 x8y0
c. y y4 y3
f. m4np5 m0n3 n2p4
5
b. 4 5 = 20 = 20
4
3
4 + 3
c. 2 + 2 = 2
2
4
= 2
2 + 4
d. 5 5 = 5
7
6
= 5 Dec 16­2:36 PM
Use the product rule to simplify:
Dec 16­2:37 PM
Can you find a pattern or shortcut from writing it all the way out each time? a. (7y5)(6y)
Multiply the coefficients together, than use the product rule for variables with the same base.
b. (­3x2y7)(5xy6)
Dec 16­2:39 PM
Dec 16­2:40 PM
Simplify the following expression using the quotient rule for exponets:
Quotient Rule
To ___________ powers with the same base, _____ the exponents. Dec 16­2:41 PM
a. b.
c.
d.
e.
f.
Dec 16­2:41 PM
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Chapter 6.1(a) Integer Exponents.notebook
January 09, 2017
When do you add exponents?
Homework
When can you subtract exponents?
Dec 16­2:44 PM
Product and Quotient Rule
Dec 17­2:33 PM
Jan 9­3:40 PM
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