Unit 4, Lesson 14
Evaluating Expressions with Exponents
Accelerated 6
Practice
Problem 1
Lin says, “I took the number 8, and then multiplied it by the square of 3.” Select all the expressions that equal the result of Lin’s operations.
\(8 \boldcdot 3^2\)
\((8 \boldcdot 3)^2\)
\(8 \boldcdot 2^3\)
\(3^2 \boldcdot 8\)
\(24^2\)
72
Problem 2
Find the value of each expression.
- \(7 + 2^3\)
- \(9 \boldcdot 3^1\)
- \(20 - 2^4\)
- \(2 \boldcdot 6^2\)
- \(8 \boldcdot (\frac{1}{2})^2\)
- \(\frac{1}{3} \boldcdot 3^3\)
- \((\frac{1}{5} \boldcdot 5)^5\)
Problem 3
Andre says, “I multiplied 4 by 5, then cubed the result.” Select all the expressions that equal the result of Andre’s operations.
\(4 \boldcdot 5^3\)
\((4 \boldcdot 5)^3\)
\((4 \boldcdot 5)^2\)
\(5^3 \boldcdot 4\)
\(20^3\)
500
8,000
Problem 4
Han has 10 cubes, and each cube has an edge length of 5 inches.
- Write an expression with an exponent that represents the total volume of Han’s cubes, in cubic inches.
- Write an expression with an exponent that represents the total surface area of Han’s cubes, in square inches.
Problem 5
Priya says that \(\frac{1}{3} \boldcdot \frac{1}{3} \boldcdot \frac{1}{3} \boldcdot \frac{1}{3} = \frac{4}{3}\). Do you agree with Priya? Explain or show your reasoning.
Problem 6
Answer each question. Show your reasoning.
- 125% of \(a\) is 30. What is \(a\)?
- 35% of \(b\) is 14. What is \(b\)?
Problem 7
Which expression represents the solution to the equation \(2.4y=13.75\)?
- \(13.75 - 2.4\)
- \((13.75) \boldcdot (2.4)\)
- \(13.75 \div 2.4\)
- \(2.4 \div 13.75\)
Problem 8
Jada explains how she finds \(15 \boldcdot 23\):
“I know that ten 23s is 230, so five 23s will be half of 230, which is 115.
15 is 10 plus 5, so \(15 \boldcdot 23\) is 230 plus 115, which is 345.”
- Do you agree with Jada? Explain your reasoning
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Draw a 15-by-23 rectangle. Partition the rectangle into two rectangles and label them to show Jada’s reasoning.