Fill in the blank(s) to correctly complete each sentence. In the expression 6^3, 6 is the ____ , and 3 is the ____ .

Verified step by step guidance

1. Identify the structure of the expression \(6^3\).
2. Recognize that in an expression of the form \(a^b\), \(a\) is the base and \(b\) is the exponent.
3. Apply this understanding to the given expression \(6^3\).
4. Determine that 6 is the base of the expression.
5. Determine that 3 is the exponent of the expression.

Key Concepts

Base

In an exponential expression, the base is the number that is being multiplied by itself. In the expression 6^3, the base is 6, which indicates that 6 will be used as a factor in the multiplication process. Understanding the role of the base is crucial for evaluating exponential expressions.

Exponent

The exponent in an exponential expression indicates how many times the base is multiplied by itself. In the expression 6^3, the exponent is 3, meaning that 6 is multiplied by itself three times (6 × 6 × 6). This concept is fundamental in understanding the growth of numbers in exponential form.

Exponential Notation

Exponential notation is a mathematical shorthand used to represent repeated multiplication of the same number. It consists of a base and an exponent, as seen in expressions like 6^3. This notation simplifies the writing and calculation of large numbers and is widely used in various mathematical applications.