Learning Goal: Write repeated multiplication as a power and evaluate powers using whole-number exponents.
Vocabulary
baseThe number being multiplied by itself in a power. In 5³, the base is 5.
exponentThe small raised number that tells how many times to use the base as a factor. In 5³, the exponent is 3.
powerA number written with a base and exponent, like 5³ (read 'five to the third power').
squaredRaised to the second power (used as a factor 2 times), like 6² = 6 × 6.
cubedRaised to the third power (used as a factor 3 times), like 2³ = 2 × 2 × 2.
What You Need to Know
An exponent tells you how many times to multiply the base by itself, NOT base × exponent.
Example: 2³ means 2 × 2 × 2 = 8, not 2 × 3 = 6.
Read 5² as 'five squared' and 4³ as 'four cubed.'
Any base to the first power equals itself: 7¹ = 7.
Powers of 10 are quick: 10² = 100, 10³ = 1000 (the exponent counts the zeros).
Evaluate the exponent first when it appears in a larger expression (order of operations).
Worked Example I Do — watch how it works
Evaluate 3⁴.
Step 1. The base is 3 and the exponent is 4, so use 3 as a factor 4 times: 3 × 3 × 3 × 3.
Step 2. Multiply two at a time: 3 × 3 = 9, then 9 × 3 = 27.
Step 3. Finish: 27 × 3 = 81.
Answer: 3⁴ = 81
Guided Practice We Do — try it together
1. Write 6 × 6 using an exponent, then evaluate.
💡 Hint: Count how many times 6 is a factor; that number is the exponent.
2. Evaluate 2⁵.
💡 Hint: Multiply 2 by itself 5 times: 2×2×2×2×2.
3. Evaluate 10³.
💡 Hint: The exponent 3 tells you the number of zeros after the 1.
Independent Practice You Do — show your work
1. Evaluate 4³.
2. Evaluate 5².
3. Write 7 × 7 × 7 as a power.
4. Evaluate 2⁴.
5. Evaluate 1⁶.
MCAP-Style Practice
Directions: Answer each item the way you would on the MCAP. For selected-response items, fill in the circle (○) next to the correct answer. For constructed-response items, enter your answer and show your work. Every item below assesses standard 6.EE.A.1.
Item 1Selected Response6.EE.A.1
Which expression is equal to 2³?
Select the correct answer.
Item 2Selected Response6.EE.A.1
What is the value of 5²?
Select the correct answer.
Item 3Constructed Response6.EE.A.1
A square floor is 8 tiles by 8 tiles. Write this as a power and find the total number of tiles.
Enter your answer in the space provided. Show your work.
Enter your answer:
Teacher Answer Key (click to show)
Independent 1
64
Independent 2
25
Independent 3
7³
Independent 4
16
Independent 5
1
Item 1 · 6.EE.A.1
C — 2³ means the base 2 used as a factor 3 times: 2 × 2 × 2 = 8.
Item 2 · 6.EE.A.1
C — 5² = 5 × 5 = 25.
Item 3 · 6.EE.A.1
8² = 64 tiles — An 8-by-8 square is 8 used as a factor twice, which is 8² = 64.
Neft Teacher · Grade 6 MCAP Mathematics Review · Standard 6.EE.A.1