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Chapter 0: Problem 72

Simplify each expression. $$ |-2-3|(-9)-4^{2} $$

Short Answer

Expert verified
-61

Step by step solution

01

- Simplify the Absolute Value

Calculate the expression inside the absolute value: |-2 - 3|Combine the terms inside the absolute value: -2 - 3 = -5Take the absolute value to get: |-5| = 5.
02

- Evaluate the Expression with the Absolute Value

Substitute the result from Step 1 into the expression: 5(-9) - 4^{2}.
03

- Multiply the Terms

Multiply 5 and -9: 5(-9) = -45.
04

- Evaluate the Exponent

Calculate the exponent 4^2: 4^{2} = 16.
05

- Combine the Results

Combine the results from Step 3 and Step 4: -45 - 16Finally, perform the subtraction: -45 - 16 = -61.

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Key Concepts

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

Understanding Absolute Value
Absolute value represents the distance a number is from zero on the number line. It is always a positive number or zero. For example, the absolute value of -5 is written as \(|-5|\), and it equals 5.

When you see \(|-2 - 3|\), start by subtracting inside the absolute value. This results in -5. Since \(|-5|\) equals 5, replace the expression with 5.

Always remember, the absolute value of any number is its non-negative counterpart.
Basics of Exponents
Exponents tell you how many times to multiply a number by itself. For example, \(4^2\) means 4 multiplied by itself, which equals 16. When you deal with exponents in expressions, calculate them before doing any addition or subtraction.

In our example, \(4^{2} = 16\).

Recall that exponents follow the PEDMAS/BODMAS rules of operation, coming right after parentheses/brackets and before multiplication and division.
Understanding Subtraction
Subtraction is the process of taking one number away from another. In our problem, after controlling absolute values and exponents, we encounter subtraction: \(-45 - 16\).

The result of subtracting 16 from -45 is -61.

When subtracting, if both numbers are negative, add their absolute values and place a negative sign in front of the sum.
Importance of Multiplication
Multiplication involves combining equal groups. In our example, \(5 \times -9\) simplifies to -45.

Multiplying a positive number by a negative number results in a negative product. Conversely, multiplying two negative numbers gives a positive result.

When multiple operations are involved, always follow the order of operations (PEDMAS/BODMAS): Parentheses/Brackets, Exponents, Multiplication and Division, Addition and Subtraction.

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Most popular questions from this chapter

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