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Chapter 0: Problem 2

For exercises 1-80, evaluate. $$ 7^{2} $$

Short Answer

Expert verified
49

Step by step solution

01

Identify the Base and Exponent

The base is 7 and the exponent is 2, which means you need to calculate 7 raised to the power of 2.
02

Understand Exponentiation

Exponentiation is repeated multiplication. Since the exponent is 2, you multiply the base by itself once: \( 7 \times 7 \).
03

Perform the Multiplication

Now calculate the multiplication: \( 7 \times 7 = 49 \).
04

Write the Final Answer

The value of \( 7^{2} \) is 49.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

base and exponent
In mathematics, when working with exponents, we have two main components: the base and the exponent. The base is the number that is being multiplied. The exponent tells you how many times to multiply the base by itself.
In the exercise above, the base is 7, and the exponent is 2.
Understanding these two parts is key to evaluating expressions correctly.
exponentiation
Exponentiation is the operation used to raise a number (the base) to a power (the exponent). It is a form of repeated multiplication. When you see an exponent, it means you multiply the base by itself a specific number of times.
In our example, 7 is the base, and it needs to be multiplied by itself because the exponent is 2. This means we calculate: \( 7 \times 7 \).
With exponentiation, the base can be any number, and the exponent can be any whole number.
multiplication
Multiplication is a fundamental arithmetic operation. It combines sums of groups of equal sizes efficiently.
When we evaluated \( 7^2 \), we performed the multiplication of 7 by itself: \( 7 \times 7 \).
This step results in the value of 49. Here, you can see how exponentiation simplifies repeated multiplication into one concise expression.

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Most popular questions from this chapter

$$ \text { Find } 1 \% \text { of } 200 \text {. } $$

For exercises \(47-58\), rewrite the percent as a decimal number. $$ 2 \% $$

For exercises 115-118, evaluate. On a scientific calculator, use the fraction key. For graphing calculators, use the Frac command to rewrite the decimal answer as a fraction. $$ \frac{5}{34}-\frac{8}{21} $$

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