Exponents
Exponents provide shorthand notation for repeated multiplication. In Grade 6 Saxon Math Course 1, the base is the number being multiplied and the exponent (or power) tells how many times to multiply it by itself. So 2⁵ means 2 × 2 × 2 × 2 × 2 = 32. Students also learn that any number to the power of zero equals 1 (e.g., 7⁰ = 1) and that any number to the power of 1 equals itself (7¹ = 7). Exponent notation is used throughout algebra, scientific notation, and area/volume formulas.
Key Concepts
New Concept Exponents are a shorthand for repeated multiplication. The exponent shows how many times the base is used as a factor.
The exponent indicates how many times the base is used as a factor. $$ 7^3 \text{ means } 7 \cdot 7 \cdot 7 $$ $$ 7^4 \text{ means } 7 \cdot 7 \cdot 7 \cdot 7 $$ What’s next This is just the beginning of working with powers. Next, you'll tackle worked examples on comparing powers and using them in prime factorization and order of operations.
Common Questions
What does the exponent tell you?
The exponent (small number raised) tells you how many times to multiply the base by itself.
Write 2 × 2 × 2 × 2 × 2 using an exponent and calculate its value.
2⁵. Value: 2 × 2 × 2 × 2 × 2 = 32.
What is 3⁴?
3 × 3 × 3 × 3 = 81.
What is any number to the zero power?
Any nonzero number raised to the power of 0 equals 1. Example: 5⁰ = 1.
What is the difference between the base and the exponent?
The base is the number being multiplied repeatedly (the larger number); the exponent is the small raised number showing how many times.