Problem 1

Question

Evaluate each expression. $$ 7^{2} $$

Step-by-Step Solution

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Answer

1Step 1: Understand Exponents

An exponent indicates how many times a base number is multiplied by itself. In the expression $7^2$, the base is 7, and the exponent is 2, which means we need to multiply 7 by itself once.

2Step 2: Multiply the Base by Itself

To evaluate $7^2$, multiply the base number 7 by itself: $7 \times 7$.

3Step 3: Calculate the Product

Now perform the multiplication: $7 \times 7 = 49$.

Key Concepts

Base NumberMultiplicationEvaluate Expressions

Base Number

In the world of exponents, the base number is fundamental. It is the number that we multiply by itself. In an expression like $7^2$, 7 is the base number. Think of it as the foundation upon which the exponent acts.

The base tells you which number will be repeatedly multiplied.
For example, in $3^3$, the base is 3. This means you will continue using the number 3 in your calculations.

Recognizing the base in different expressions is crucial for evaluating them correctly, as it ensures we understand what number we are working with.

Multiplication

Multiplication is a key operation when dealing with exponents. When an expression involves an exponent, it indicates repeated multiplication of the base number.

For instance, with $7^2$, the exponent 2 tells us to multiply 7 by itself.
This can be visualized as: 7 × 7.

Understanding this concept helps simplify what might initially seem like complex operations. Remember, multiplication in exponents is simply repeated addition.

Evaluate Expressions

Evaluating expressions with exponents means performing the indicated operations to get a numerical result. This involves breaking down the exponent into more manageable steps.

First, identify the base and the exponent.
Next, perform the multiplication as instructed by the exponent. For $7^2$, this means doing the calculation $7 \times 7$.
Finally, solve to get the product, which in this case is 49.

By following these steps, you can evaluate any expression involving exponents, transforming it from abstract notation to a real number.

Problem 1

Other exercises in this chapter

Problem 1

Complete each table for each polynomial. See Example 1. $$ x^{2}-3 x+5 $$ $$ \begin{array}{|c|c|} \hline \text { Term } & \text { Coefficient } \\ \hline x^{2}

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Simplify each expression. Write each result using positive exponents only. $$ 4^{-3} $$

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Multiply. $8 x^{2} \cdot 3 x$

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Problem 2

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