Lesson 14
Expressions with Exponents
Let's use the meaning of exponents to decide if equations are true.
Problem 1
Select all expressions that are equal to \(3 \boldcdot 3 \boldcdot 3 \boldcdot 3 \boldcdot 3\).
\(3 \boldcdot 5\)
\(3^5\)
\(3^4 \boldcdot 3\)
\(5 \boldcdot 3\)
\(5^3\)
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.
 \(4 \boldcdot 5\)
 \(4+5\)
 \(4^5\)
 \(5^4\)
Problem 3
Decide whether each equation is true or false, and explain how you know.
 \(9 \boldcdot 9 \boldcdot 3 = 3^5\)
 \(7 + 7 + 7 = 3 + 3 + 3 + 3 + 3 + 3 + 3\)
 \(\frac{1}{7} \boldcdot \frac{1}{7} \boldcdot \frac{1}{7} = \frac{3}{7}\)
 \(4^1 = 4 \boldcdot 1\)

\(6 + 6 + 6 = 6^3\)
Problem 4
 What is the area of a square with side lengths of \(\frac35\) units?
 What is the side length of a square with area \(\frac{1}{16}\) square units?
 What is the volume of a cube with edge lengths of \(\frac23\) units?
 What is the edge length of a cube with volume \(\frac{27}{64}\) cubic units?
Problem 5
Select all the expressions that represent the area of the shaded rectangle.
\(3(10c)\)
\(3(c10)\)
\(10(c3)\)
\(10(3c)\)
\(303c\)
\(3010c\)
Problem 6
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.
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.