**Learning Targets:**

- I can decide if expressions with exponents are equal by evaluating the expressions or by understanding what exponents mean.

**Related Pages**

Illustrative Math

Grade 6

Let’s use the meaning of exponents to decide if equations are true.

Illustrative Math Unit 6.6, Lesson 13 (printable worksheets)

The following diagram gives some examples of exponents with bases that are fractions, decimals, and variables.

Which one doesn’t belong?

2 · 2 · 2 · 2

16

2^{4}

4 · 2

Scroll down the page for the solutions to the “Are you ready for more?” section.

Decide whether each equation is true or false, and explain how you know.

- 2
^{4}= 2 · 4 - 3 + 3 + 3 + 3 + 3 = 3
^{5} - 5
^{3}= 5 · 5 · 5 - 2
^{3}= 3^{2} - 16
^{1}= 8^{2} - ½ · ½ · ½ · ½ = 4 · ½
- (½)
^{4}= ⅛ - 8
^{2}= 4^{3}

In each list, find expressions that are equivalent to each other and explain to your partner why they are equivalent. Your partner listens to your explanation. If you disagree, explain your reasoning until you agree. Switch roles for each list.

(There may be more than two equivalent expressions in each list.)

What is the last digit of 3^{1,000} Show or explain your reasoning.

- Select all expressions that are equal to 3 · 3 · 3 · 3 · 3

A. 3 · 5

B. 3^{5}

C. 3^{4}· 3

D. 5 · 3

E. 5^{3} - Noah starts with 0 and then adds the number 5 four times. Diego starts with 1 and then multiplies by the number 5 four times. For each expression, decide whether it is equal to Noah’s result, Diego’s result, or neither.

A. 4 · 5

B. 4 + 5

C. 4^{5}

D. 5^{4} - Decide whether each equation is true or false, and explain how you know.

a. 9 · 9 · 3

b. 7 + 7 + 7 = 3 + 3 + 3 + 3 + 3 + 3 + 3

c. 1/7 · 1/7 · 1/7 = 3/7

d. 4^{1}= 4 · 1

e. 6 + 6 + 6 = 6^{3} - a. What is the area of a square with side lengths of 3/5 units?

b. What is the side length of a square with area 1/16 square units?

c. What is the volume of a cube with edge lengths of 2/3 units?

d. What is the edge length of a cube with volume 27/64 cubic units? - Select all the expressions that represent the area of the shaded rectangle.

A. 3(10 - c)

B. 3(c - 10)

C. 10(c - 3)

D. 10(3 - c)

E. 30 - 3c

F. 30 - 10c - A ticket at a movie theater costs $8.50. One night, the theater had $29,886 in ticket sales.

a. Estimate about how many tickets the theater sold. Explain your reasoning.

b. How many tickets did the theater sell? Explain your reasoning. - A fence is being built around a rectangular garden that is 8 1/2 feet by 6 1/3 feet. Fencing comes in panels. Each panel is 2/3 of a foot wide. How many panels are needed? Explain or show your reasoning.

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.

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