Lesson 5: Exponents and Order of Operations

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.

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 $\frac{1}{4} \cdot \frac{1}{4} = \frac{1}{16}$.

Property

When evaluating expressions containing exponents, follow the order of operations (PEMDAS): Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Pay special attention to the difference with negative bases:

• $(-a)^n$ means the base is $-a$
• $-a^n$ means the base is $a$, and you take the opposite of the result