Exponents
Exponents introduces the notation where an exponent tells how many times the base factor is used in a repeated multiplication: bⁿ means b multiplied by itself n times. Covered in Yoshiwara Elementary Algebra Chapter 5: Exponents and Roots, Grade 6 students learn that the base is the repeated factor and the exponent (or power) is the count of repetitions. Understanding exponent notation is foundational for all work with powers, polynomials, scientific notation, and the laws of exponents.
Key Concepts
Property An exponent is a number that appears above and to the right of a particular factor. It tells us how many times that factor occurs in the expression. The factor to which the exponent applies is called the base , and the product is called a power of the base. An exponent indicates repeated multiplication. $$a^n = a \cdot a \cdot a \cdots a \quad (n \text{ factors of } a)$$ where $n$ is a positive integer.
Examples To compute $5^3$, we multiply three factors of 5: $5 \cdot 5 \cdot 5 = 125$.
The expression $(\frac{1}{4})^2$ means $\frac{1}{4} \cdot \frac{1}{4} = \frac{1}{16}$.
Common Questions
What is an exponent?
An exponent is a small number written above and to the right of a base that tells how many times the base is multiplied by itself. For example, 4³ = 4 × 4 × 4 = 64.
What is the difference between the base and the exponent?
The base is the number being multiplied repeatedly. The exponent (or power) tells how many times the base appears as a factor.
What does any number to the power of 1 equal?
Any number raised to the power of 1 equals itself: a¹ = a.
Where are exponents introduced in Yoshiwara Elementary Algebra?
Exponents are introduced in Chapter 5: Exponents and Roots of Yoshiwara Elementary Algebra.
What does a zero exponent mean?
Any nonzero base raised to the power of 0 equals 1: a⁰ = 1. This is a convention derived from the exponent laws.