Exponents and Exponential Notation

Definition and Purpose of Exponents

Exponent notation provides a concise way to represent repeated multiplication of the same number. In this notation, the base is the number being multiplied, and the exponent (or power) is the small number written above and to the right of the base, indicating how many times the base is used as a factor.

• Base: The number being multiplied repeatedly.

• Exponent (Power): Indicates the number of times the base is multiplied by itself.

For example, the expression 8 × 8 × 8 × 8 can be written as $8^4$.

This is read as "eight to the fourth power." More generally, if a number b is multiplied by itself n times, it can be expressed as $b^n$, or "b to the nth power."

Evaluating Exponential Expressions

Exponent notation not only simplifies writing but also aids in understanding and calculating values. To find the value of an exponential expression, expand it into repeated multiplication.

• Example 1: $7^2$ (seven squared) means $7 \times 7 = 49$.

• The exponent 2 is often called "squared," and the exponent 3 is called "cubed."

• Example 2: $10^3$ (ten cubed), which expands to $10 \times 10 \times 10$.

• Calculating step-by-step: $10 \times 10 = 100$, then $100 \times 10 = 1,000$. Thus, $10^3 = 1,000$.