Problem 2 - Elementary Algebra

Question

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

Step-by-Step Solution

Answer

49

Step 1: 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.

Step 2: Understand Exponentiation

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

Step 3: Perform the Multiplication

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

Step 4: Write the Final Answer

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

Key Concepts

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.