# Lesson 13

Expressions with Exponents

### Problem 1

Select all expressions that are equal to $$3 \boldcdot 3 \boldcdot 3 \boldcdot 3 \boldcdot 3$$.

A:

$$3 \boldcdot 5$$

B:

$$3^5$$

C:

$$3^4 \boldcdot 3$$

D:

$$5 \boldcdot 3$$

E:

$$5^3$$

### Solution

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### Problem 2

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.

1. $$4 \boldcdot 5$$
2. $$4+5$$
3. $$4^5$$
4. $$5^4$$

### Solution

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### Problem 3

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

1. $$9 \boldcdot 9 \boldcdot 3 = 3^5$$
2. $$7 + 7 + 7 = 3 + 3 + 3 + 3 + 3 + 3 + 3$$
3. $$\frac{1}{7} \boldcdot \frac{1}{7} \boldcdot \frac{1}{7} = \frac{3}{7}$$
4. $$4^1 = 4 \boldcdot 1$$
5. $$6 + 6 + 6 = 6^3$$

### Solution

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### Problem 4

1. What is the area of a square with side lengths of $$\frac35$$ units?
2. What is the side length of a square with area $$\frac{1}{16}$$ square units?
3. What is the volume of a cube with edge lengths of $$\frac23$$ units?
4. What is the edge length of a cube with volume $$\frac{27}{64}$$ cubic units?

### Solution

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### Problem 5

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:

$$30-10c$$

### Solution

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(From Unit 6, Lesson 10.)

### Problem 6

A ticket at a movie theater costs $8.50. One night, the theater had$29,886 in ticket sales.

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

2. How many tickets did the theater sell? Explain your reasoning.

### Solution

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(From Unit 5, Lesson 13.)

### Problem 7

A fence is being built around a rectangular garden that is $$8 \frac{1}{2}$$ feet by $$6 \frac{1}{3}$$ feet. Fencing comes in panels. Each panel is $$\frac{2}{3}$$ of a foot wide. How many panels are needed? Explain or show your reasoning.

### Solution

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(From Unit 4, Lesson 12.)