Expressions with Exponents

Grade 6 · algebra · 95 practice problems · read aloud

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What Are Exponents? 🤔

An exponent tells you how many times to multiply a number (the base) by itself. It's a shortcut for repeated multiplication! For example, instead of writing 5 × 5 × 5, we write 5³. This is super useful for writing very large numbers efficiently.

How to Solve Problems with Exponents

  1. Identify the Base and Exponent: In 4², 4 is the base and 2 is the exponent.
  2. Multiply the Base: Multiply the base by itself as many times as the exponent says. For 4², you do 4 × 4.
  3. Calculate: Solve the multiplication problem you created.

Worked Examples

Example 1: 2⁴

Step 1: Base = 2, Exponent = 4.

Step 2: Multiply: 2 × 2 × 2 × 2.

Step 3: Calculate: (2×2)=4, (4×2)=8, (8×2)=16.

Answer: 2⁴ = 16

Example 2: 5² + 3³

Step 1: Solve each part separately. 5² = 5 × 5 = 25.

Step 2: 3³ = 3 × 3 × 3 = 27.

Step 3: Add the results: 25 + 27 = 52.

Answer: 52

Common Mistakes to Avoid ⚠️

Multiplying the base and exponent: 4² is NOT 4 × 2 = 8. It is 4 × 4 = 16.

Forgetting the "1" Rule: Any number to the power of 1 is itself. 9¹ = 9, not 1.

Order of Operations: Remember PEMDAS! Exponents come before multiplication, division, addition, and subtraction.

Tips & Tricks

  • Memory Aid: The exponent is like the "repetition counter."
  • Squares are Special: A power of 2 is called "squared." 6² is "six squared."
  • Power of 0: Any number (except 0) to the power of 0 is 1. 10⁰ = 1, 150⁰ = 1.

How to Practice

To get better at exponents, try these activities:

  • Flashcards: Make cards with expressions like 7² on the front and the answer on the back.
  • Create a Table: Write out the squares of numbers 1 through 12.
  • Solve Real Problems: "If a square garden has sides of 8 feet, the area is 8² square feet. What is the area?"

Practice problems

6 of the 95, worked through step by step — try them before opening the answer.

1 3³ + 5² = ?

Hint: Evaluate each exponent separately first, then add the results together.

Show the answer

Answer: 52

  1. Evaluate 3³. 3³ = 3 × 3 × 3 = 27.
  2. Evaluate 5². 5² = 5 × 5 = 25.
  3. Add the results: 27 + 25 = 52.

The answer is 52.

2 4³ + 5² = ?

Hint: Remember to evaluate each exponent separately before adding. An exponent tells you how many times to multiply the base by itself.

Show the answer

Answer: 89

  1. Evaluate 4³. This means 4 × 4 × 4 = 16 × 4 = 64.
  2. Evaluate 5². This means 5 × 5 = 25.
  3. Add the results: 64 + 25 = 89.

The answer is 89.

3 7³ + 9² = ?

Hint: Evaluate the exponent first: find the value of 7 cubed, then find the value of 9 squared. Finally, add the two results together.

Show the answer

Answer: 424

  1. Evaluate 7³. 7³ = 7 × 7 × 7 = 49 × 7 = 343.
  2. Evaluate 9². 9² = 9 × 9 = 81.
  3. Add the results: 343 + 81 = 424.

The answer is 424.

4 4³ + 6² = ?

Hint: Evaluate each exponent separately first, then add the results together.

Show the answer

Answer: 100

  1. Evaluate 4³. 4³ = 4 × 4 × 4 = 16 × 4 = 64.
  2. Evaluate 6². 6² = 6 × 6 = 36.
  3. Add the results: 64 + 36 = 100.

The answer is 100.

5 6³ + 8² = ?

Hint: Evaluate each exponent separately first, then add the results together.

Show the answer

Answer: 280

  1. Evaluate 6³. 6³ = 6 × 6 × 6 = 36 × 6 = 216.
  2. Evaluate 8². 8² = 8 × 8 = 64.
  3. Add the results: 216 + 64 = 280.

The answer is 280.

6 5³ + 10² = ?

Hint: First, evaluate each exponent separately by multiplying the base by itself the number of times shown by the exponent. Then add the two results together.

Show the answer

Answer: 225

  1. Evaluate 5³. This means 5 × 5 × 5. 5 × 5 = 25, then 25 × 5 = 125.
  2. Evaluate 10². This means 10 × 10 = 100.
  3. Add the results: 125 + 100 = 225.

The answer is 225.

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