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Magazine Chapter 9: Problem 32
Perform each indicated operation. $$ (-12)^{2}+(-1)(2)-6 $$
Short Answer
Expert verified
The result is 136.
Step by step solution
01
Evaluate the Exponentiation
The expression begins with \((-12)^2\). To perform this, multiply \(-12\) by itself: \(-12 \times -12 = 144\). So, \((-12)^2 = 144\).
02
Perform Multiplication
Next, handle the multiplication \((-1)(2)\). Multiply \(-1\) and \(2\): \(-1 \times 2 = -2\).
03
Substitute Results into Expression
Substitute the results from Steps 1 and 2 back into the expression: \(144 + (-2) - 6\).
04
Perform Addition
Now perform the addition of \(144\) and \(-2\): \(144 + (-2) = 142\).
05
Perform Final Subtraction
Finally, subtract \(6\) from \(142\): \(142 - 6 = 136\).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Exponentiation
Exponentiation is an important mathematical operation where a number is raised to the power of another number. In simple terms, it means multiplying a number by itself a certain number of times. The expression \((-12)^2\) means multiplying \(-12\) by itself. \(-12 \ imes \ -12 = 144\). Keep in mind:
Always square the entire base including the sign, as shown in the problem.
- An even power (such as 2) of a negative number (like -12) results in a positive outcome. This is why the square of \(-12\) is \144\.
- The base number is \(-12\), and the exponent is \2\.
Always square the entire base including the sign, as shown in the problem.
Multiplication
Multiplication is the process of adding a number to itself repeatedly. In our expression, we have \((-1)(2)\), which means \-1\ is multiplied by \2\. To compute:
In problems involving multiple operations, multiplication is usually calculated before addition and subtraction according to the order of operations.
- The product of \-1\ and \2\ is \-2\, since multiplying any number by \-1\ inverts its sign.
- This shows a pivotal property of multiplication with negative numbers. The result takes the negative sign of \-1\.
In problems involving multiple operations, multiplication is usually calculated before addition and subtraction according to the order of operations.
Addition and Subtraction
Addition and subtraction are fundamental arithmetic operations. In the expression \(144 + (-2) - 6\), we need to handle these with care:
This procedure ensures correct computation and is essential for maintaining numerical accuracy.
- Adding \(-2\) is like subtracting \2\: \144 + (-2) = 142\.
- After applying addition, subtract \6\ from \142\ to get \136\.
This procedure ensures correct computation and is essential for maintaining numerical accuracy.
Integer Operations
Integer operations cover addition, subtraction, multiplication, and exponentiation when dealing with whole numbers. Understanding the behavior of integers, particularly with different signs, is critical:
Practicing operations involving integers bolsters proficiency in tackling more complex mathematical challenges.
- Positive integers increase the value when added, while negative integers decrease it.
- Multiplying two negative integers results in a positive product, while a negative and a positive produces a negative outcome.
- Subtraction of integers is essentially the addition of a negative value.
Practicing operations involving integers bolsters proficiency in tackling more complex mathematical challenges.
