Problem 45 - Algebra 1

Question

Evaluate the expression. \(3 \cdot 3 \cdot 3 \cdot 3 \cdot 3\)

Step-by-Step Solution

Answer

The result of \(3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \) or \(3^5\) is 243.

Step 1: Identifying the operation

The exercise consists of multiplying the number 3 by itself, 5 times. This can be written as \(3 \cdot 3 \cdot 3 \cdot 3 \cdot 3\), or more simply as \(3^5\).

Step 2: Performing the operation

Next the task is to perform the operation. In this case, \(3^5\) equals to 243.

Key Concepts

Evaluate Expressions

Understanding how to evaluate expressions is a foundational skill in mathematics. Evaluating an expression means to calculate the value of the expression by performing the operations it includes. For example, consider the expression given in the textbook exercise:

To evaluate this expression, you need to recognize the repeated multiplication of the same number, which is 3, multiplied by itself five times. The operation involved is multiplication, and the expression simplifies to a single numerical value once the operation is performed. It's like following a recipe, where each step (multiplication, in this case) must be followed in sequence to reach the final product, which is the number 243.

Exponential Notation

Exponential notation is a convenient way to represent repeated multiplication of the same number. Instead of writing the number multiple times, you can express it using a base and an exponent. In our example, the base is 3, and the exponent is 5, represented as \(3^5\). This expression communicates that the number 3 is used as a factor 5 times in the multiplication. It's a kind of mathematical shorthand that makes it easier to read and work with expressions involving repeated multiplication. Learning to interpret and use exponential notation simplifies complex calculations and is a powerful tool as you delve into more advanced mathematics.

Multiplication of Numbers

Multiplication of numbers is one of the basic arithmetic operations and signifies repeated addition. In our textbook example, we deal with the multiplication of the number 3 by itself multiple times. It's like saying you have 5 groups of 3 and want to know how many you have in total.

When you multiply numbers together, you find the product, which in this case is 243. Multiplication can sometimes be simplified using exponentiation, especially when the same number is being multiplied by itself repeatedly. This operation is fundamental not only in basic arithmetic but also in many algebraic contexts. As you progress in math, you'll find multiplication to be a building block for more complex concepts.