Transcript 2.1 .what is a power

What is a Power?
Topic
2.1
A POWER is an expression in the form an,
where a is the BASE and n is the
EXPONENT.


The BASE is the number (or variable) that is
multiplied by itself
The EXPONENT tells you how many time
you will multiply the base
Examples




Base = 7
Exponent = 3
Power = 73
Repeated Multiplication = 7 x 7 x 7
Examples




Base = 9
Exponent = 5
Power = 95
Repeated Multiplication = 9 x 9 x 9 x 9 x 9
Examples




Base = y
Exponent = 4
Power = y4
Repeated Multiplication = y x y x y x y
Examples




Base = -3
Exponent = 4
Power = (-3)4
Repeated Mult = (-3) x (-3) x (-3) x (-3)
A power with a integer base and an
exponent of 2 is a SQUARE NUMBER
5cm
5x5= 52
=25
5cm 25 is a square
number
Example:
To find the area of a
square, we use s2.
A power with a integer base and an
exponent of 3 is a CUBE NUMBER
5cm
5cm
5cm
5x5x5= 53
=125
125 is a cube
number
Example:
To find the volume of a
cube, we use s3.
Some Definitions

Standard Form  Simply just written as a
number. No exponents!

Repeated Multiplication  Writing out a
power as a multiplication statement.
Examples
Write as a POWER.
a)
b)
3x3x3x3x3x3x3 = 37
7 = 71
Write as a repeated multiplication and in standard form.
a)
b)
29 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 512
114 = 11 x 11 x 11 x 11 = 14641
Solving powers with a
NEGATIVE BASE

We solve it the same way. We must be
careful to INCLUDE the negative sign.
EX: (-3)3
= (-3) x (-3) x (-3)
= -27
Is my answer positive or negative?

If you have an EVEN number of negative
signs your answer is POSITIVE
example: (-)(-) = + (-)(-)(-)(-) = +
(-9) x (-9) = 81 (-2) x (-2) x (-2) x (-2) = 16

If you have an ODD number of negative
signs your answer is NEGATIVE
example: (-)(+) = (-9) x (9) = -81
(-)(-)(-) = (-2) x (-2) x (-2) = -8
Examples:
**Brackets are VERY Important
1) Identify the base of each power,
then evaluate.
a) (-3)4
base: -3
= (-3)(-3)(-3)(-3) = 81
(even # of negatives) (4)
*the exponent applies to the negative sign
Examples:
**Brackets are VERY Important
b) -34
base: 3
= (-1) (3x3x3x3) = -81
(odd # of negatives) (1)
*the exponent does NOT apply to the
negative sign
*the negative sign in front is like multiplying
by -1 (after exponent is solved – order of
operations)
Examples:
**Brackets are VERY Important
c) – (-3)4
base: -3
= (-1) (-3)(-3)(-3)(-3) = -81
(odd # of negatives) (5)
*the exponent applies to the negative sign
in the bracket but not the one in front of
it
Ways to write multiplications

Use the multiplication sign (x)
7 x 7 x 7 = 343

Brackets
(7)(7)(7) = 343

Variables
ab = a x b = (a)(b)
Making your life simpler!!!
** On your calculator use the ^ symbol to
solve a power
7^3 = 343
Assignment
Page 55-57
#4ac, 5ac, 7, 8, 9, 10, 13, 14acegik,
17abcd, 18a, 21a