## Exponents and Roots

##### Created by:

djc225  on June 23, 2012

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# Exponents and Roots

 Adding or subtracting terms with same base ex: 2³+2⁵Pull out the common factor: 2³+2⁵ = 2³(1+2²)
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#### Definitions

Adding or subtracting terms with same base
ex: 2³+2⁵
Pull out the common factor:
2³+2⁵
= 2³(1+2²)
Adding or subtracting terms with different bases:
ex: 2³+6³
Break down bases and pull out common factor:
2³+6³
=2³ + (2·3)³
=2³ + 2³·3³
=2³(1+3³)
Squares to memorize:

11²
12²
13²
14²
15²
20²
30²
1² = 1
11² = 121
12² = 144
13² = 169
14² = 196
15² = 225
20² = 400
30² = 900
Cubes to memorize

10³
1³ = 1
2³ = 8
3³ = 27
4³ = 64
5³ = 125
10³ = 1000
Powers of 2:

2⁴
2⁵
2⁶
2⁷
2⁸
2⁹
2¹⁰
2³ = 8
2⁴ = 16
2⁵ = 32
2⁶ = 64
2⁷ = 128
2⁸ = 256
2⁹ = 512
2¹⁰ = 1024
Other Powers

3⁴

3³ = 27
3⁴ = 81
4³ = 64
5³ = 125
Exponents come before negative signs:
-3²
(-3)²
-3² = - (3²) = -9
(-3)² = 9
Negative Numbers raised to positive power are always positive. Negative numbers raised to odd power are always negative....
An even exponent can hide the sign of the base.

ex: x²=16
x²=16
x can = 4 or -4
Multiply Terms with same base
ex: a²·a³
ex: 2³·
...
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