Problem 73 Simplify. $$ -8^{2}-3 $$... [FREE SOLUTION]

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Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 10: Problem 73

Simplify. $$ -8^{2}-3 $$

Short Answer

Expert verified

-67

Step by step solution

Evaluate the exponent

First, calculate the value of the exponent. Here, we have oeq 8^{2} which equals eq 64.

Apply the negative sign

Next, apply the negative sign to the result. eq -64.

Subtract 3

Finally, subtract 3 from -64. So, we have eq -64 - 3 eq -67.

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Key Concepts

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

Order of Operations

The order of operations is a critical concept in simplifying expressions. It's a set of rules that dictates the sequence in which you should perform different mathematical operations. Here's a handy acronym to remember the order: PEMDAS.

Parentheses
Exponents
Multiplication and Division
Addition and Subtraction

PEMDAS helps ensure that everyone solves expressions the same way. In the expression $ -8^{2}-3 $, we start by evaluating the exponent, following the order of operations.

Exponents

Exponents are used to indicate that a number should be multiplied by itself a certain number of times. In our problem, $8^2$ means that 8 is multiplied by itself: $8 \times 8 = 64$.

This is an important step in simplifying expressions because it affects the order in which we handle the numbers. Notice that even if the base of the exponent is negative, it鈥檚 the value of the exponent we calculate first.

Negative Numbers

Negative numbers can sometimes be tricky. In this exercise, $ -8^2 $ can confuse many students. When you see a negative sign outside of an exponent, it means the negative sign is applied after calculating the exponent. For instance, $8^2=64$ and then the negative sign makes it $-64$ afterwards.

It doesn鈥檛 mean that you鈥檙e squaring a negative number. That's because of the order of operations. If it was inside parentheses, like $(-8)^2$, it would be different and it would equal 64 because $-8 \times -8 = 64$.

Subtraction

Once the exponent and negative sign are handled, we move to subtraction. Subtraction simply means taking one number away from another. In our problem, we subtract 3 from -64.

This can be written as $-64 - 3$. When you subtract a positive number from a negative number, you are essentially adding the absolute value of the positive number to the negative number. Hence $-64 - 3 = -67$.

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91影视

Simplify. $$ -8^{2}-3 $$

Short Answer

Step by step solution

Evaluate the exponent

Apply the negative sign

Subtract 3

Key Concepts

Order of Operations

Exponents

Negative Numbers

Subtraction

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