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Chapter 1: Problem 7

Find the value of each exponential expression. $$ 3^{2} $$

Short Answer

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9

Step by step solution

01

Identify the base and exponent

In the expression \(3^2\), the base is \(3\) and the exponent is \(2\).
02

Interpret the exponent

The exponent \(2\) indicates that the base \(3\) should be multiplied by itself \(2\) times.
03

Perform the multiplication

Multiply \(3\) by itself: \(3 \times 3 = 9\).

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Key Concepts

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

exponents
When dealing with exponential expressions, it is crucial to understand the role of exponents. An exponent is a small number placed to the upper-right of a base number. It tells us how many times to multiply the base by itself. For example, in the expression \(3^2\), the exponent is \(2\). This means that the base number \(3\) should be multiplied by itself a total of \(2\) times. This can be written as \(3\times 3\).
base
The base of an exponential expression is the number that is being multiplied. It is the main number in the formula. In our given example, \(3^2\), the base is \(3\). The base is crucial because it is the 'foundation' of the multiplication process. The exponent tells us how many times to use the base in the multiplication, but the base itself is what鈥檚 being repeatedly multiplied.
multiplication
Multiplication is the arithmetic operation you perform when dealing with exponents. In an expression like \(3^2\), once you recognize the base \(3\) and the exponent \(2\), the next step is to perform the multiplication. You multiply the base by itself as many times as indicated by the exponent. So, for \(3^2\), you calculate \(3 \times 3\), which results in \(9\). This process will give you the value of the exponential expression.

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