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Chapter 10: Problem 76

Simplify. $$ 20+4^{3} \div(-8) $$

Short Answer

Expert verified
12

Step by step solution

01

Evaluate the exponent

First, evaluate the exponent in the expression. Here, raise 4 to the power of 3. \( 4^3 = 64 \)
02

Perform the division

Next, perform the division operation with the result from Step 1. Divide 64 by -8. \( 64 \div (-8) = -8 \)
03

Add the results

Finally, add 20 to the result from Step 2. \( 20 + (-8) = 12 \)

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Key Concepts

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

Order of Operations
Understanding the order of operations is vital for solving algebraic expressions correctly. To easily remember the correct sequence, use the acronym PEMDAS:

  • P: Parentheses
  • E: Exponents
  • M: Multiplication
  • D: Division
  • A: Addition
  • S: Subtraction

When simplifying, always start with operations inside parentheses (if any). Then handle exponents. Next, perform multiplication and division as they appear from left to right. Finally, complete any addition and subtraction from left to right.

In our example, 20 + 4^(3) / (-8), we follow PEMDAS. First, we deal with the exponent (4^3), then the division (result divided by -8), and finally the addition (adding 20).
Exponents
Exponents are used to represent repeated multiplication of a number by itself. The expression 4^3, for instance, means multiplying 4 by itself three times: 4 * 4 * 4.

Calculating 4^3 works as follows:
  • First multiplication: 4 * 4 = 16
  • Second multiplication: 16 * 4 = 64

Thus, 4^3 = 64. In the original problem, we replaced 4^3 with 64 as instructed by the order of operations.

Remembering how to calculate and simplify exponents is crucial. Always handle exponents early in the process to avoid mistakes in the final result.
Division of Integers
Division of integers involves splitting one number by another. When dealing with positive and negative numbers, remember these rules:

  • Positive 梅 Positive = Positive
  • Negative 梅 Negative = Positive
  • Positive 梅 Negative = Negative
  • Negative 梅 Positive = Negative

In the problem, we needed to divide 64 by -8. Applying our rules, a positive number divided by a negative number results in a negative number:
64 梅 (-8) = -8.

Understanding how to divide integers accurately helps in achieving correct results in algebraic expressions. Use these simple rules to guide your division calculations effectively.

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Most popular questions from this chapter

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Multiply. \(\left(\frac{4}{5}\right)\left(-\frac{2}{3}\right)\left(-\frac{15}{7}\right)\left(\frac{1}{2}\right)\)

Simplify. $$ 8[(6-13)-11] $$
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