exponents. location of exponent an exponent is a little number high and to the right of a regular or...
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Exponents
Location of Exponent
• An exponent is a little number high and to the right of a regular or base number.
3 4Base
Exponent
Definition of Exponent
• An exponent tells how many times a number is multiplied by itself.
3 4Base
Exponent
What an Exponent Represents
• An exponent tells how many times a number is multiplied by itself.
34= 3 x 3 x 3 x 3
How to read an Exponent
• This exponent is read three to the fourth power.
3 4Base
Exponent
How to read an Exponent
• This exponent is read three to the 2nd power or three squared.
3 2Base
Exponent
How to read an Exponent
• This exponent is read three to the 3rd power or three cubed.
3 3Base
Exponent
What is the Exponent?
2 x 2 x 2 = 23
What is the Exponent?
3 x 3 = 3 2
What is the Exponent?
5 x 5 x 5 x 5 = 54
What is the Base and the Exponent?
8 x 8 x 8 x 8 = 8 4
What is the Base and the Exponent?
7 x 7 x 7 x 7 x 7 =7 5
What is the Base and the Exponent?
9 x 9 = 9 2
How to Multiply Out an Exponent to Find the
Standard Form
= 3 x 3 x 3 x 33
927
81
4
What is the Base and Exponentin Standard Form?
4 2= 16
What is the Base and Exponentin Standard Form?
2 3= 8
What is the Base and Exponentin Standard Form?
3 2= 9
What is the Base and Exponentin Standard Form?
5 3= 125
Product law:
add the exponents together when multiplying the powers with the same base.
Ex:NOTE:
This operation can only be done if the base is the same!
15
312
312
3
3
3*3
Quotient law
subtract the exponents when dividing the powers with the same base.
Ex: NOTE:
This operation can only be done if the base is the same!9
312
312
3
3
33
Power of a power:
keep the base and multiply the exponents.
Ex:
15
5*3
53
4
4
)4(
NOTE:
Multiply the exponents, not add them!
Zero exponent law:
Any power raised to an exponent of zero equals one.
Ex:
1
2141234123483 0
NOTE:
No matter how big the number is, as long as it has zero as an exponent, it equals to one. Except 100
Negative exponents:
To make an exponent positive, flip the base.
Ex:
4096
1
8
1
84
4
NOTE:
This does not change the sign of the base.
Multiplying Polynomials:
In multiplying polynomials, you have to multiply the coefficients and add up the exponents of the variables with the same base.
Ex:
35
3
2
5
32
232
20
*
*
20
5*4
45
yx
y
yy
x
xx
yxyx
Dividing polynomials:
When dividing polynomials, you must divide the coefficients(if possible) and subtract the exponents of the variables with the same base.
Ex:
2
2
24
45
24
45
5
5
525
5
25
xy
y
yy
x
xx
yx
yx
Please simplify the following equations:
Answer:5x
How?:5
32
32 * xx
Please simplify the following equations:
Answer:
513 xx
8x
How?: 8
513
Please simplify the following equations:
Answer:
How?:
255
9765625
510
9765625
5
10
5*2
10
Please simplify the following equations:
Answer:
How?:
35
125
1
5
13
125
1
5
1
5
1
5
1
5
1
53
3
Please simplify the following equations:
)3)(4( 3224 yxyx
Answer:5612 yx
How?:
56
5
32
6
24
12
*
*
12
3*4
yx
y
yy
x
xx
Please simplify the following equations:
22
43
4
12
yx
yx
Answer: 23xy
How?:
2
24
23
3
3
412
xy
yy
x
xx
Review
Copy and complete each of the following questions.
•1.) b2 * b7 •1.) b9 •2.) (p3)4 •2.) p12 •3.) (a2)3 * a3 •3.) a9
•4.) x2 * (xy)2 •4.) x4y2 •5.) (4m)2 * m3
•5.) 16m5 •6.) (3a)3*(2p)2
•6.) 108a3p2
•7.)82*(xy)2*2x •7.) 128x3y2 •8.) w3 * (3w)4 •8.) 81w7 •9.) q0 •9.) 1
•10.) p-2 •10.) 1/p2 •11.)(a2b)0 •11.) 1 •12.)(x-2y3)-2
•12.) x4/y6
•13.) p4
p2 •13.) p2 •14.) 3b2
9b5 •14.) 1/3b3
•15.) (4x2)2
4x4 •15.) 4
•16.) x2 * y0 * 32 x3 * y-4
•16.) 9y4/x
•17.) m 3 * m2n-4 n
•17.) m5/n7 •18.) 3a2 3 2b-1
b * 32 * a •18.) 6a5/b4
•19) (3/4)3 •19) 27/64 •20) 2+3(4)2 •20) 50