Exponents and Order of Operations Review & Practice

EXPONENT

BASE

EXPANDED FORM:

STANDARD FORM:

Word Form:

__________ to the _______

power.

EXPONENTIAL FORM

3x3x3x3

81

Three

Fourth

EXPONENT

Tells you how many times to
multiply the base times itself.
Example 5³ = 5 x 5 x 5

BASE

The number being multiplied

EXPANDED
FORM

Shows the base being
multiplied times itself.
Example: 4 x 4 x 4

RULES

Any number with an

exponent of zero is equal

to 1.

4⁰ = 1

5⁰ = 1

Any number with an
exponent of 1 is equal to
that number.

5¹ = 5 because the
exponent tells us there
is ONE 5.

Definitions and Rules

Multiple Choice

Identify the exponent: $$6^3$$  

• 6

• 3

Multiple Choice

Identify the base: $$4^2$$  

• 4

• 2

Multiple Choice

Which expression is equivalent to 6² - 2³?

• (6 - 2) x 5

• (6 x 6) - (2 x 2 x 2)

• (6 x 2) - (2 x 3)

• (6 + 6) - (2 + 2 + 2)

Multiple Choice

Find the value: $$3^3$$  

• 9

• 27

• 81

Multiple Choice

Find the value: $$2^4$$  

• 8

• 16

• 2

Multiple Choice

Anything raised to a power of zero is always: 

• 0

• 1

• itself

• negative

Multiple Choice

Find the equivalent expression.

15×15×15×15x12x12

• 15⁴x12²

• 4¹⁵x2¹²

• 15x4x12x2

• 15⁴+12²

​What is the order of operations?

1. ​Solve anything inside of grouping symbols ( ) { } these are parenthesis and brackets

2. Solve for exponents

3. ​Going from left to right solve any multiplication and division, which ever comes first

4. ​Going from left to right solve any addition or subtraction, which ever comes first.

Multiple Choice

(15 ÷ 3)² + 9 ÷ 3

• 11.3

• 28

• 13

Multiple Choice

27 ÷ 3 x 2 + 4²

• 34
• 20.5
• 26

Multiple Choice

Find and explain the error.    
 5 - 3 + 2
     5 - 5
        0

• There is no error.
• Addition was done first and you should have subtracted first
• There is a subtraction error

​Remember...

• First, do everything inside parentheses or brackets

• Next, do any exponents, like x²

• Perform any multiplication or division from left to right​

• Last, solve any addition or subtraction from left to right

​

Take it step by step!

Multiple Choice

Which operation would you do first?
( 12 + 10) ÷ 10 · 14 - 6

• Division
• Multiplication
• Addition
• Subtraction

Multiple Choice

Evaluate the equation:
5 · 2 - (11 - 7)

• 10
• 4
• 6
• 11

Multiple Choice

2(1.5 + 2.5)

• 8
• 5.5
• 6

Multiple Choice

3 x 8 - (9 - 7)³

• 16
• 18
• 0

Multiple Select

Click all the expressions that combined like terms CORRECTLY.

• n + 4 − 9 − 5n

  =

  16n + 3

• 12r + 5 + 3r − 5

  =

  28r + 10

• −2x + 11 + 6x

  =

  4x + 11

Multiple Choice

Are 7x and 5y like terms?

• No, they have different variables.

• Yes, they have the same variables.

Multiple Choice

Simplify the following expression:

7x+5x

• x

• 7x

• 12x

The Distributive Property Steps

• Multiply each number inside the ( ) by the number outside the ( )

• Combine like terms if necessary

• Remember the integer rules for multiplying and adding/subtracting

Distributive Property

• multiply the number on the outside of ( ) to everything on the inside of ( )

• 6( a + 4)

• (multiply 6 times a) + (multiply 6 times 4)

• 6 times a= 6a

• 6 times 4 = 24

• final answer: 6a + 24

Multiple Select

Click all the expressions that combined like terms CORRECTLY.

• n − 4 − 9

  =

  n − 13

• 4n − n

  =

  5n

• 5n + 11n

  =

  16n