Exponents

Grades 6-9 · Concept Explainer

Key Points

✓An exponent indicates how many times a base is multiplied by itself.
✓The base is the number being multiplied, and the exponent is the number of times it's multiplied.
✓Any number raised to the power of 1 is equal to itself (e.g., 7¹ = 7).
✓Any non-zero number raised to the power of 0 is equal to 1 (e.g., 4⁰ = 1).
✓Exponents simplify writing repeated multiplication.

Exponents are a shorthand way of writing repeated multiplication. Instead of writing 2 x 2 x 2, we can write 2³. The small number, 3, is the exponent, and the larger number, 2, is the base. The exponent tells you how many times to multiply the base by itself. For example, 5² (read as "5 squared") means 5 x 5, which equals 25. Similarly, 2⁴ (read as "2 to the power of 4") means 2 x 2 x 2 x 2, which equals 16. Understanding exponents is crucial for algebra and other advanced math topics.

Worked Example

Evaluate 3⁴

Step 1: Identify the base and the exponent. The base is 3 and the exponent is 4.
Step 2: Write out the repeated multiplication: 3 x 3 x 3 x 3
Step 3: Perform the multiplication: 3 x 3 = 9, then 9 x 3 = 27, and finally 27 x 3 = 81

Answer: 81

Try It Yourself

1. Evaluate 2³

2. Evaluate 5² + 10

3. Evaluate (4²) / 2 + 3⁰

Watch Out For These Mistakes

Multiplying the base by the exponent instead of repeated multiplication (e.g., thinking 2³ = 2 x 3 = 6).
Forgetting that any number to the power of 0 equals 1.
Incorrectly applying the order of operations when exponents are involved.