Introduction to Exponents
Introduction to Exponents is a Grade 6-7 math skill that introduces students to exponential notation as a shorthand for repeated multiplication. Students learn to evaluate expressions with whole number exponents, identify the base and exponent, and apply exponents to powers of 10.
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 tells you how many times to multiply the base by itself. For example, 3 to the 4th power = 3 times 3 times 3 times 3 = 81.
What is the base and what is the exponent?
In 5 squared, 5 is the base and 2 is the exponent. The base is the number being multiplied, and the exponent tells how many times.
What does it mean to raise a number to the second power?
Raising a number to the second power (squared) means multiplying it by itself once: 4 squared = 4 times 4 = 16.
What is any number to the power of zero?
Any nonzero number raised to the power of zero equals 1. For example, 7 to the 0 = 1.
What grade introduces exponents?
Exponents are introduced in Grade 5-6 and developed in Grade 7 math.