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Let's start with understanding what a base number is in exponential notation. The base number is the number that is being multiplied repeatedly. Think of it as the foundation in exponential expressions. In the expression given in the exercise, the base number is 13 because it is the number being multiplied by itself. The base number remains the same as long as the same number is being used in the multiplication. It's the key to understanding the entire expression.
For example, in the expression 13 * 13 * 13, the base is 13. This means we are dealing with 13 as our primary number, and this will be crucial when converting it to exponential notation.

Next, let's talk about the exponent. The exponent is a small number written above and to the right of the base number. It tells you how many times the base number is multiplied by itself. You can think of it as a shorthand way of showing repeated multiplication. In our example, since 13 is multiplied 3 times, the exponent is 3.
When we write it using exponential notation, it looks like this: \( 13^3 \). The exponent simplifies the expression and makes it easier to read and work with. Instead of writing 13 * 13 * 13, you simply write 13 followed by a superscript 3.

In this section, we dive into multiplication and how it relates to exponential notation. Multiplication is basically repeated addition. For example, 3 * 4 means adding 3 four times (3 + 3 + 3 + 3). Exponential notation takes this idea further to repeated multiplication.
In our problem, multiplying 13 by itself three times (13 * 13 * 13) can be simplified using exponential notation. Instead of repeatedly writing the same number in a long multiplication, you write the base number once and use an exponent to show how many times it is multiplied.
This makes the expression more compact and much easier to understand. Multiplication and exponents are intertwined, as exponents offer a simplified and efficient way to handle large multiplication problems.