1. exponents - livingston public schools · 2015-09-28 · 1. exponents september 28, 2015...
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1. Exponents September 28, 2015
Exponentsexponent 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.
Vocabulary you should know....
n0 =1 any number to the 0 power = 1 except 00 which is undefined
n1 = n
Special Cases
any number to the firstpower = itself
variable – a symbol or letter that represents a number that can change or is unknownEx. x, z, r, π, Θ
constant a value that does not change (not affected by a variable) Ex. 7, 19, 208
algebraic expression contains one or more variables and may contain operation symbols and constantsEx. 8n, 27x + n, 15y2
coefficient a factor that is multiplied to a variableEx. 27y 12x 5n
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.
x2y3 =
Variables are written in alphabetical order
coefficients are written before variables
5x2y3z2 =
When variables and/or constants in parentheses are raised to an exponent, everything in the parentheses are raised to that power.
5n2(xy)3=
Ex.
Ex.
Ex.
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
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 =
More Exponents: Squares and Cubes
Square and cube are the only two numbers that have special names. For the rest of the numbers we say....
1. Exponents September 28, 2015
Write the following in exponential form, then solve.
fourteen cubed=
seven squared=
nine to the 4th power= theta cubed=
three cubed plus eleven squared= Clicker Problems for today and yesterday
1. twelve squared2. nine cubed3. three squared4. 525. 2 cubed6. 437. 6 to the second power8. Do you know what a perfect square number is?
1. Exponents September 28, 2015
Perfect Square Numbers
n n2 2
1
23
4
5
Perfect Square Numbers
11
12
13
14
15
16
17
18
19
20
n n2 = n
1
2
3
4
5
6
7
8
9
10
n n2 = n
11 121
12 144
13 169
14 196
15 225
16 256
17 289
18 324
19 361
20 400
n n2 = n n n2 = n
1 1
2 4
3 9
4 16
5 25
6 36
7 49
8 64
9 81
10 100
Powers of Ten in Exponential Form
100 = 10 ● 10 = 102
one hundred thousand= 100,000 = 10●10●10●10●10 = 105
10 8 = 100,000,000 = one hundred million
The exponent is the number of zeroes!
Practice Write each numeral in exponential form or vice versa a. one trillion
b. 107
c. 10,000,000,000,000,000
d. 109
e. 100 quintillion
f. 1018
g. 10 million
h. 1010
1,000,000,000,000 = 1012
10,000,000
= 1016
1,000,000,000
100,000,000,000,000,000,000 = 1020
1,000,000,000,000,000,000 one quintillion
10,000,000 = 107
10,000,000,000 = ten billion
erase toreveal
1. Exponents September 28, 2015
Zero as an exponent
Any number raised to the zero power is 1, except 00 is undefined.