DAILY WARMUP 1. (-12)² = 2. -4³ = 3. What is the base? 36⁸ 4. What is the exponent? 72⁸ 5. (3 + 7)³ = 144 -64 36 8 1000

Exponents An exponent tells how many times a number is multiplied by itself. Base 11⁵ Exponent

Expanded Form Expanded Form – A number is written in expanded form when the base is multiplied the number of times indicated by the exponent. Write 86 in expanded form. 8 ∙ 8 ∙ 8 ∙ 8 ∙ 8 ∙ 8 You try it! Write (-2)5 in expanded form. -2 ∙ -2 ∙ -2 ∙ -2 ∙ -2

Exponential Form Exponential Form – a number is in exponential form when it is written with a base and an exponent. Write 9 ∙ 9 ∙ 9 ∙ 9 in exponential form. 9⁴ Write 7 ∙ 7 ∙ 7 ∙ 7 ∙ 7 ∙ 7 in exponential form. 7⁶

X0 = 1 990= 1 Examples: 20=1 Zero Rule Any non-zero number raised to the zero power equals one X0 = 1 Examples: 20=1 990= 1 That seems wrong! Anything to the zero power is equal to 1 !?!? …Well click on the information button for an explanation!

Any number raised to the power of one equals itself. Rule of One Any number raised to the power of one equals itself. x1=x Examples: 171 = 17 991 = 99 Well this one is easy!

Multiplying Exponents

What does this expression really mean? 53 ∙ 54

What does this expression really mean? 53 ∙ 54 5 ∙ 5 ∙ 5

What does this expression really mean? 53 ∙ 54 5 ∙ 5 ∙ 5 5 ∙ 5 ∙ 5 ∙ 5

What does this expression really mean? 53 ∙ 54 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5

What does this expression really mean? 53 ∙ 54 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 = 57

What does this expression really mean? 53 ∙ 54 = 57 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 = 57

Let’s look at another example. 35 ∙ 34

Let’s look at another example. 35 ∙ 34 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3

Let’s look at another example. 35 ∙ 34 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 3 ∙ 3 ∙ 3 ∙ 3

Let’s look at another example. 35 ∙ 34 = 39 39 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 =

From these 2 examples, we can draw a conclusion. 3 + 4 = 7 53 ∙ 54 = 57 When multiplying with two bases that are the same, keep the base and add the exponents. . 5 + 4 = 9 35 ∙ 34 = 39

Simplify each expression. 1) 47 ∙ 45 = 2) 82 ∙ 80 = 3) c3 ∙ c = 4) (5xy2)(-4x3y5) = 5) (3x2)(2x3) =

Simplify each expression. 1) 47 ∙ 45 = 412 2) 82 ∙ 80 = 82 3) c3 ∙ c = c4 4) (5xy2)(-4x3y5) = -20x4y7 5) (3x2)(2x3) = 6x5

Dividing Exponents

What does this expression really mean? 56 ÷ 53

What does this expression really mean? 56 ÷ 53 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 5 ∙ 5 ∙ 5

What does this expression really mean? 56 ÷ 53 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 5 ∙ 5 ∙ 5

What does this expression really mean? 56 ÷ 53 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 5 ∙ 5 ∙ 5

What does this expression really mean? 56 ÷ 53 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 5 ∙ 5 ∙ 5

What does this expression really mean? 56 ÷ 53 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 5 ∙ 5 ∙ 5 = 53

What does this expression really mean? 56 ÷ 53 = 53 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 5 ∙ 5 ∙ 5 = 53

Let’s look at another example. 47 ÷ 42

Let’s look at another example. 47 ÷ 42 4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 4 ∙ 4

Let’s look at another example. 47 ÷ 42 4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 4 ∙ 4

Let’s look at another example. 47 ÷ 42 4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 4 ∙ 4

Let’s look at another example. 47 ÷ 42 4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 4 ∙ 4 = 45

Let’s look at another example. 47 ÷ 42 = 45 4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 4 ∙ 4 = 45

From these 3 examples, we can draw a conclusion. 6 – 3 = 3 56 ÷ 53 = 53 When dividing with two bases that are the same, you can simply subtract the exponents. 7 – 2 = 5 47 ÷ 42 = 45

Simplify each expression. 47 ÷ 45 = 82 ÷ 80 = c3 ÷ c = 24k9 6k5 = 5) 32 · 24 · 45 = 31 · 22 · 43

Simplify each expression. 47 ÷ 45 = 42 82 ÷ 80 = 82 c3 ÷ c = c2 24k9 6k5 = 4k4 5) 32 · 24 · 45 31 · 22 · 43 = 192