Lesson 13

Expressions with Exponents

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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.

Area diagram. Rectangle partitioned into two smaller rectangles. One rectangle shaded blue.
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.)