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Chapter 1: Problem 11

Find the value of each exponential expression. $$ 12^{2} $$

Short Answer

Expert verified
144

Step by step solution

01

Identify the base and exponent

In the expression \( 12^{2} \), 12 is the base and 2 is the exponent.
02

Understand what the exponent means

The exponent 2 means that the base 12 is multiplied by itself 2 times. So, \( 12^{2} \) is the same as \( 12 \times 12 \).
03

Perform the multiplication

Calculate \( 12 \times 12 = 144 \).
04

Write down the final answer

The value of \( 12^{2} \) is 144.

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Key Concepts

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

Base and Exponent
Understanding the components of an exponential expression is essential. In any expression like \(12^2\), there are two key parts: the base and the exponent.
The base is the number that is being multiplied, which in this case is 12.
The exponent is the number that tells you how many times to multiply the base by itself, which here is 2.
So for \(12^2\), the base (12) will be multiplied by itself as many times as indicated by the exponent (2).
Multiplication
When dealing with exponents, understanding multiplication is crucial. In our example, \(12^2\) means you need to multiply the base 12 by itself 2 times.
This is because the exponent 2 tells us the number of times to repeat the base in a multiplication.
So, \(12^2 = 12 \times 12\).
This calculation simplifies to 144.
Multiplication might seem basic, but it forms the backbone of working with exponents effectively.
Solving Exponents
Solving exponents involves a few simple steps. First, you identify the base and the exponent as we did with \(12^2\).
Next, understand what the exponent is asking you to do鈥攎ultiply the base by itself the number of times indicated by the exponent.
For \(12^2\), you'd multiply 12 by 12.
This gives you 144, which is the final answer.
Always write down each step to minimize mistakes, making your calculations clear and methodical.

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Most popular questions from this chapter

Write each sentence as an equation, using \(x\) as the variable. Then find the solution from the set of integers between \(-12\) and \(12,\) inclusive. See Example \(9 .\) 6 less than a number is 4

Write a numerical expression for each phrase and simplify. See Examples 7 and \(8 .\) Two-thirds of the difference between 8 and \(-1\)

Write each sentence as an equation, using \(x\) as the variable. Then find the solution from the set of integers between \(-12\) and \(12,\) inclusive. See Example \(9 .\) 7 less than a number is 2

Write a numerical expression for each phrase and simplify. 1.85 more than the sum of \(-1.25\) and \(-4.75\)

Decide whether each statement is true or false. \(-|12|>|-15|\)
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