Order of Operations with Integers and Exponents

​Exponents and Order of Operations

By the end of this lesson,

​You will be able to:

• Understand that a power is a repeated multiplication

• Identify the base and exponent of a power

• Write a power in expanded form (repeated multiplication)

• Evaluate an exponent

• Solve expressions (with exponents) using the order of operations

Exponents are repeated multiplication:

3³ = 3 x 3 x 3

The exponent (the small raised number) tells you HOW MANY times to multiply the base.

7³ = 7 x 7 x 7

Multiple Choice

Which number is the BASE?

5⁴

• 4

• 5

Multiple Choice

Which number is the BASE?

2³ = 8

• 2

• 3

• 8

Multiple Choice

Which number is the EXPONENT?

2³ = 8

• 2

• 3

• 8

Fill in the Blank

Identify the EXPONENT:  $$4^3$$  

Multiple Choice

$$4^{3\ }$$  

Write in expanded form:

• 4x4x4

• 4+4+4

• 3x3x3x3

• 3+3+3+3

Fill in the Blank

$$4^3$$  

Evaluate

Multiple Choice

$$2^4$$  

Write in expanded form:

• 4x4

• 4+4

• 2x2x2x2

• 2+2+2+2

Fill in the Blank

$$2^4$$  

Multiple Choice

How would you rewrite this number in exponential form?

2 x 2 x 2 x 2

• 2 x 4

• 2 ⁴

• 4²

• 2

Multiple Choice

Find the equivalent expression.

9 x 9 x 9 x 9 x 9

• 9⁵

• 9¹⁵

• 9 x 5

• 9 + 9 + 9 + 9+ 9

Multiple Choice

2⁵ is the same as 2 x 5.

• True

• False

Multiple Choice

How is 6 squared represented as an exponent?

• 6 x 2

• $$6^2$$

• 6 x 3

• $$6^3$$

Multiple Select

$$6^3$$  is read....

• 6 to the 3

• 6 cubed

• 6 to the third power

• 3 to the sixth power

• 6 cubed

​Order of Operations

Vocabulary

• Numerical Expression - expression containing only numbers and operations

• Evaluate - find the value of (solve)

• Order of Operations - set of rules used to evaluate numerical expressions

Multiple Select

Evaluate means to ___________.

• Solve

• Rewrite

• find the value of

Order of Operations

Order of Operations

• Perform operations in Parentheses

• Evaluate numbers with Exponents

• Multiply or Divide from left to right

• Add or Subtract from left to right

Multiplication can be represented with

Multiple Choice

Evaluating parentheses is the ___________ step when following order of operations.

• first

• second

• third

• fourth

Multiple Choice

Evaluating exponents is the ___________ step when following order of operations.

• first

• second

• third

• fourth

Multiple Choice

Evaluating multiplication and division is the ___________ step when following order of operations.

• first

• second

• third

• fourth

Multiple Choice

Evaluating addition and subtraction is the ___________ step when following order of operations.

• first

• second

• third

• fourth

Example:

Example:

Multiple Choice

$$36\ \div\ 2^2\ -\ 1\ \times\ 2^3$$  

• 1

• 64

• 4,096

Multiple Choice

$$6^2\ \div\ 3^2\ \times\ 2^3$$  

• 32

• 18

• 0.5

• 1

Multiple Choice

Evaluate: $$6\times15-10\div2$$  

• 40

• 85

• 60

Multiple Choice

Evaluate:

$$5^2-5\left(10-5\right)$$  

• $130
• 100

• 0

Fill in the Blank

You have four $10 bills and eighteen $5 bills in your piggy bank. How much money do you have?

Poll

I can identify the base and the exponent of a power.

• Yes!

• Mostly

• A little bit

• No!

Poll

I can write an exponent in expanded form.

• Yes!

• Mostly

• A little bit

• No!

Poll

I can evaluate an exponent.

• Yes!

• Mostly

• A little bit

• No!

Poll

I can evaluate an expression using the order of operations.

• Yes!

• Mostly

• A little bit

• No!