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1. Exponents
September 28, 2015
Vocabulary you should know....
Exponents
exponent ­ a number that indicates how many times the base is used as a factor. Writing exponents is a shorthand notation to show multiplication. 53 means 5• 5• 5 3 is the exponent. base ­ a number used as a factor in an exponential expression. In the expression 73 , 7 is the base. Special Cases
n1 = n
any number to the firstpower = itself
variable – a symbol or letter that represents a number that can change or is unknown
Ex. x, z, r, π, Θ
constant ­ a value that does not change (not affected by a variable) Ex. 7, 19, 208 n0 =1 any number to the 0 power = 1 except 00 which is undefined
coefficient ­ a factor that is multiplied to a variable
Ex. 27y 12x 5n algebraic expression ­ contains one or more variables and may contain operation symbols and constants
Ex. 8n, 27x + n, 15y2
Writing algebraic expressions as repeated multiplication When there is no symbol between variables and/or constants it means multiplication. There MUST be symbols between two constants. Variables are written in alphabetical order Ex. x2y3 = coefficients are written before variables
Ex. 5x2y3z2 =
When variables and/or constants in parentheses are raised to an exponent, everything in the parentheses are raised to that power. Ex. 5n2(xy)3=
Try This! First show the extended form of the exponent. Then solve.
54=
1. Exponents
September 28, 2015
75=
1451=
t8=
23k4=
140=
Write the following in exponential form
7 7 7 7 7 7 Θ Θ Θ Θ
1. Exponents
September 28, 2015
More Exponents: Squares and Cubes square ­ n2 , raising to the power of 2, multiplying a value by itself. 62 = 6 ∙ 6 = 36 42 = 9 2 = x2 = cube ­ n3 , raising to the power of 3, multiplying three of the same value by itself.
23 = 2 ∙ 2 ∙ 2 = 8
43 = 5 3 = y3 = Square and cube are the only two numbers that have special names. For the rest of the numbers we say....
1. Exponents
Write the following in exponential form, then solve. September 28, 2015
seven squared=
fourteen cubed=
nine to the 4th power=
three cubed plus eleven squared= theta cubed=
Clicker Problems for today and yesterday
1. twelve squared
2. nine cubed
3. three squared
4. 52
5. 2 cubed
6. 43
7. 6 to the second power
8. Do you know what a perfect square number is?
1. Exponents
September 28, 2015
Perfect Square Numbers
Perfect Square Numbers
n
1
n2
2
n n2
= n
n n2
1
11
2
12
2
3
3
13
4
14
5
15
6
16
4
7
17
8
18
5
9
19
10
20
= n
Powers of Ten in Exponential Form n
n
1
1
2
4
3
9
4
16
5
25
= n
2
n
n2
11
121
= n
100 = 10 ● 10 = 102
one hundred thousand= 100,000 = 10●10●10●10●10 = 105
12 144
13 169
10
14 196
The exponent is the number of zeroes! 15 225
6
36
7
49
8
64
17 289
9
81
18 324
16 256
19 361
10 100
20 400
Practice ­ Write each numeral in exponential form or vice versa a. one trillion 1,000,000,000,000 = 1012
b. 107 10,000,000 c. 10,000,000,000,000,000 d. 109
1,000,000,000 e. 100 quintillion f. 1018 100,000,000,000,000,000,000 = 1020
1,000,000,000,000,000,000 one quintillion
g. 10 million h. 1010 = 1016
10,000,000 = 107
10,000,000,000 = ten billion
erase to
reveal
8
= 100,000,000 = one hundred million
1. Exponents
September 28, 2015
Zero as an exponent
Any number raised to the zero power is 1, except 00 is undefined.