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Chapter 1: Problem 44

Evaluate each expression. $$(-1)(2-8)^{3}$$

Short Answer

Expert verified
The expression evaluates to 216.

Step by step solution

01

Simplify Inside the Parentheses

First, simplify the expression inside the parentheses: determine the value of 2 - 8. Therefore, \(2 - 8 = -6\).
02

Raise to the Power

Next, take the result from step 1, which is \(-6\), and raise it to the power of 3: \[ (-6)^3 = (-6) \times (-6) \times (-6) \].First compute: \((-6) \times (-6) = 36\). Then, multiply by \(-6\) again: \[ 36 \times (-6) = -216 \].So, \((-6)^3 \) equals \(-216\).
03

Multiply by -1

Finally, multiply the result from step 2, which is \(-216\), by -1: \((-1) \times (-216) = 216\).Therefore, the expression evaluates to 216.

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Key Concepts

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

Parentheses Simplification
When evaluating mathematical expressions, always start by simplifying inside the parentheses. This is the first rule of operations known as PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).

For example, in the expression \((-1)(2-8)^3\), you should first handle the parentheses.

Inside the parentheses, you have \((2 - 8)\).

Subtract 8 from 2, resulting in \(-6\). So now, the expression becomes \((-1)(-6)^3\).
Raising to a Power
The next step is to raise the number to a given power. When you see an expression like \((-6)^3\), it means you need to multiply -6 by itself three times.

Start by multiplying -6 by -6. This gives you 36 because a negative times a negative is a positive.

Next, take that result (36) and multiply by -6 again. This time, you'll get -216.

Therefore, \((-6)^3 = -216\).
Multiplication of Integers
The final step in the given exercise is to multiply the result of the previous step by -1. Let's revisit the expression \((-1)(-6)^3\).

Remember, from the second step, we found that \((-6)^3 = -216\). Now, multiply this result by -1.

\((-1) \times (-216) = 216\).

Multiplying a negative by a negative results in a positive. So, the final answer is 216.

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