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Which is equivalent to x15?
a. (x3)(x5)b. (x3)5
c. (3x)(5x)d. (x2)(x4)/x21
7
5 4
4
4
3
1. 3
2. x
3. (x + 3)
34.
5
y
1. (4)(4)(4)(4)(4)(4)
2. (-2x)(-2x)(-2x)(-2x)
3. (x+1)(x+1)(x+1)
4. (w)(w)(w)(p)(p)(p)(p)(p)
Examples: -5 x-4xabc8
Non-Examples: p + q c/d a – b 2b – 4c + x
A monomial is a number, variable, or product of a number and one or more variables.
Exploring Monomial Rules
In groups of 4 …
(x3)(x2)
1. Expand the expression using the definition of exponent.
2. Rewrite the expanded form using exponents.
3. Compare #1 to #2. what operation can be used on the exponent in #1 to get the exponent in #2?
(32x2y)(3x2y3)
1. Expand the expression using the definition of exponent.
2. Rewrite the expanded form using exponents.
3. Compare #1 to #2. what operation can be used on the exponent in #1 to get the exponent in #2?
- Multiplying like bases: To multiply two powers that have the same base, add the exponents.
22 ● 23 = = 2 ● 2 ● 2 ● 2 ● 2 = 25
1. a4 ● a3
2. (4ab6)(-7a2b3)
1. Expand the expression using the definition of exponent.
2. Rewrite the expanded form using exponents.
3. Compare #1 to #2. what operation can be used on the exponent in #1 to get the exponent in #2?
5
2
w
w
1. Expand the expression using the definition of exponent.
2. Rewrite the expanded form using exponents.
3. Compare #1 to #2. what operation can be used on the exponent in #1 to get the exponent in #2?
6 18 27
2 23 15
5
5
k w
k w
Dividing like bases: to divide powers that have the same base, subtract the exponents.
For all integers, m and n and any nonzero number a,
mm n
n
aa
a
7 4
2
62p np n
7
15
bb
6
4
xyy x
To find the power of a product, find the power of each factor and multiply.
(-2xy)3 == (-23)(x3)(y3)= -2 ● -2 ● -2 ● x ● x ● x ●y
● y ●y= -8x3y3
1. Expand the expression using the definition of exponent.
2. Rewrite the expanded form using exponents.
3. Compare #1 to #2. what operation can be used on the exponent in #1 to get the exponent in #2?
33
4
b
w
1. Expand the expression using the definition of exponent.
2. Rewrite the expanded form using exponents.
3. Compare #1 to #2. what operation can be used on the exponent in #1 to get the exponent in #2?
2 5( )h t
To find the power of a power, multiply the exponents:
(22)3 == (22)(22)(22)= 2 ● 2 ● 2 ● 2 ● 2 ●
2 = 26
3
2
6 2
3
28 161) 2)
16 18
8 30g3) 4)
8 51
z n
z n p
h
g
Your Turn
To find the power of quotient, find the power of the numerator and the power of the denominator.
For any integer m an any real numbers a and b, b 0,
( ) .m
mn
a a
b b
34=
33=
32=
31=
1. Complete the first 4 rows of the table.
2. Describe the patterns in each column
3. Based on your observation, continue the pattern for the columns of the table.
4. Look at the row with the zero exponent. Describe what you see.
5. Look at the rows with negative exponents. Describe what you see.
For any real number a and any integer n where n 0,
1nn
aa
1 nna
a
Example #1:
5-2 = 2
1 1
5 25
3
2 5
7
1
4
x
x yz
Any non zero number, raised to the zero power equals 1.
0
0
05
7
2 1
1
31
8
x
x yxy
05
2
3
8
x y
xy
3 0t z
(a3)7
(x4)12
[(32)3]4
(3x2y3)5
(-2v3w4)3(-3vw3)2
Which is equivalent to x15?
a. (x3)(x5)b. (x3)5
c. (3x)(5x)d. (x2)(x4)/x21
322a ba
34 4
2 2
43p qp q
45 3
4 3
2v wv w
46 3
5
32r sr s
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