Lesson 1: Exponents

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

Step 1. Parentheses and Other Grouping Symbols
Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first.
Step 2. Exponents
Simplify all expressions with exponents.
Step 3. Multiplication and Division
Perform all multiplication and division in order from left to right. These operations have equal priority.
Step 4. Addition and Subtraction
Perform all addition and subtraction in order from left to right. These operations have equal priority.

Examples

• To simplify $30 - 5 \cdot 4$, we perform multiplication first: $30 - 20 = 10$.
• In the expression $(3+2)^2 \div 5$, we start with parentheses $(5)^2 \div 5$, then the exponent $25 \div 5$, and finally division to get $5$.
• For $4 + 2[10 - 3(2)]$, we work inside the innermost parentheses first: $4 + 2[10 - 6]$, then inside the brackets $4 + 2[4]$, then multiply $4 + 8$, and finally add to get $12$.

Explanation

The order of operations (PEMDAS) is a set of rules everyone follows to solve math problems. This ensures that every expression has only one correct answer, preventing confusion and making sure our calculations are consistent.