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Exploring Exponents and Powers
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Exploring Exponents and Powers
Read each exponent as repeated multiplication. Show your calculations when asked.
Understanding Exponents
1.Which repeated-multiplication expression does 2³ represent?
- 2 + 3
- 2 × 3
- 2 × 2 × 2
- 3 × 3
2.Choose the expression equal to 4⁵.
- 4 × 5
- 4 × 4 × 4 × 4 × 4
- 5 × 5 × 5 × 5
- 4 + 4 + 4 + 4 + 4
3.What is the value of 10²?
- 20
- 100
- 12
- 102
4.In 6⁴, what is the name for the 6, and what is the name for the 4?
5.Complete the powers of 10: 10³ = and 10⁴ = .
Calculate and Compare Powers
6.Calculate 2⁵.
7.Calculate 3³.
8.Calculate 6².
9.Calculate 4³.
10.Which is greater, 2⁶ or 5²? Work out both values to support your choice.
11.A set of 8 switches can each be either on or off. The number of possible switch settings is 2⁸. How many settings are possible?
Powers in Context
12.A digital game doubles the number of coins in a bonus pile each round. If the pile starts with 1 coin, write an exponent expression for the number of coins after 7 rounds, then find the total.
13.In your own words, explain why writing 3⁴ can be more convenient than writing 3 × 3 × 3 × 3. Include what 3⁴ equals.
14.Complete the first four positive powers of 4: 4¹ = , 4² = , 4³ = , and 4⁴ = .
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