Grade 6 | Unit 6 | Lesson 13: Expressions with Exponents | Practice Problems

Select all expressions that are equal to 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3.

• 3 \cdot 5

• 3^5

• 3^4 \cdot 3

• 5 \cdot 3

• 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. \

\\\\ \\\\ \\\\ \\\\ \\\\ \

Expression	Result
4 \cdot 5	Noah’s
4+5	Neither
4^5	Neither
5^4	Diego’s

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

• 9 \cdot 9 \cdot 3 = 3^5

• 7 + 7 + 7 = 3 + 3 + 3 + 3 + 3 + 3 + 3

• \frac{1}{7} \cdot \frac{1}{7} \cdot \frac{1}{7} = \frac{3}{7}

• 4^1 = 4 \cdot 1

• 6 + 6 + 6 = 6^3

What is the area of a square with side lengths of \frac{3}{5} units? What is the side length of a square with area \frac{1}{16} square units?

• $\frac{9}{25}$ square units (\frac{3}{5} \times \frac{3}{5} = \frac{9}{25})

• \frac{1}{4} units (\frac{1}{4} \times \frac{1}{4} = \frac{1}{16})

What is the volume of a cube with edge lengths of \frac{2}{3} units? What is the edge length of a cube with volume \frac{27}{64} cubic units?

• $\frac{8}{27}$ cubic units (\frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} = \frac{8}{27})

• \frac{3}{4} units (\frac{3}{4} \times \frac{3}{4} \times \frac{3}{4} = \frac{27}{64})

Select all the expressions that represent the area of the shaded rectangle.

• 3(10-c)

• 3(c-10)

• 10(c-3)

• 10(3-c)

• 30-3c

A ticket at a movie theater costs $8.50. One night, the theater had $29,886 in ticket sales. Estimate about how many tickets the theater sold. Explain your reasoning.

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

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.