1. Any number raised to the power of 1 is that number
One as Exponent
Any number raised to the power of 1 is that number
x1 = x
61 = 6

2. Any non-zero number raised to the power of 0 is equal to 1.
Zero as Exponent
Any non-zero number raised to the power of 0 is equal to 1.
x0 = 1
70 = 1

3. Negative One as Exponent Write the base as its reciprocal
x-1 = 1/x
4-1 = 1/4

4. Multiplication of Powers
Powers of the same base may be multiplied by adding their exponents.
xmxn = xm+n
x2x3 = x2+3 = x5

5. Powers of the same base may be divided by subtracting their exponents.
Division of Powers
Powers of the same base may be divided by subtracting their exponents.

6. Powers of Powers
Powers of the same base may be raised to another power by multiplying their exponents.
(xm)n = xmn
(x2)3 = x2×3 = x6

7. Apply the exponent to every term inside the parentheses
Product to a Power
Apply the exponent to every term inside the parentheses
(xy)n = xnyn
(2y)3 = 23y3 =8y3

8. Dividing different bases with the same exponent
The exponent gets applied to both parts of the fraction – numerator & denominator
= 16 𝑦 2

9. 𝑥 −3 = 1 𝑥 3 Negative Exponents
The base gets written as the reciprocal and the power becomes positive on the denominator
x-n = 1/xn
𝑥 −3 = 1 𝑥 3

10. Different Bases raised to the same power
Multiply the bases together and raise the product to that power
(x)n(y)n = (xy)n
(4)3(t)3 = (4t)3

11. Commutative Property of Addition
As long as the numbers are all being added together, you can change the order of your numbers.
a+b+c = a+c+b
6+3+4 = 6+4+3
9+4 = 10+3
13 = 13

12. Associative Property of Addition
As long as the numbers are all being added together, you move the parentheses to regroup the numbers.
(a+b)+c = a+(b+c)
(7+2)+8 = 7+(2+8)
(9)+8 = 7+(10)
17 = 17

13. Property of Multiplication
Associative
Property of Multiplication
As long as the numbers are all being multiplied together, you move the parentheses to regroup the numbers.
(a·b)·c = a·(b·c)
(5·9)·2 = 5·(9·2)
(45)·2 = 5·(18)
90 = 90

14. Property of Multiplication
Commutative
Property of Multiplication
As long as the numbers are all being multiplied together, you can change the order of your numbers.
a·b·c = a·c·b
2·7·5 = 2·5·7
14·5 = 10·7
70 = 70

15. Distributive Property
The Distributive Property lets you multiply a sum by multiplying each addend separately and then add the products.
a(b+c) = ab+ac
13(2+8) = 13·2+13·8