Problem 39 Simplify using the order of oper... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 2: Problem 39

Simplify using the order of operations. $$\left[(-8)^{2}-5^{2}\right] \div(-4+1)$$

Short Answer

Expert verified

-13

Step by step solution

Simplify Exponents

First, simplify the exponents. Calculate $(-8)^2$ and $5^2$ separately. \[(-8)^{2} = 64 \] and \[5^{2} = 25 \]

Perform Subtraction Inside the Brackets

Next, subtract $5^2$ from $(-8)^2$. \[64 - 25 = 39 \] So the expression inside the brackets is simplified to 39.

Simplify Inside the Parentheses

Now, simplify the expression inside the parentheses: $-4 + 1$. \[-4 + 1 = -3 \] So, the expression is now \[\frac{39}{-3} \]

Perform the Division

Finally, divide 39 by -3. \[39 \div -3 = -13 \] So the simplified expression is -13.

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Key Concepts

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

Simplifying Exponents

When simplifying exponents, we deal with the base and the exponent individually. The exponent tells us how many times to multiply the base by itself.
For example, $(-8)^2$ means multiplying \-8 \times -8\, which equals 64 because \-8 \times -8 = 64\.
This is because multiplying two negative numbers gives a positive result. Similarly, $5^2$ means $5 \times 5$, which equals 25.
Always remember to simplify the exponents first, as they take precedence in the order of operations.

Performing Arithmetic Operations

Once we have simplified the exponents, the next step is to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).
In our example, after finding $(-8)^2 = 64$ and $5^2 = 25$, we perform the subtraction inside the brackets: \64 - 25\.
This equals 39.
Remember the correct order: first handle operations inside parentheses or brackets, then take care of exponents.

Division

The final step is to handle division.
In our example, after simplifying the inside of the brackets to 39, we then divide by the simplified value of the parentheses term $-4 + 1 = -3$.
This gives us \39 \div -3\, which equals -13.
Division follows multiplication in the order of operations.
In division, dividing a positive number by a negative number results in a negative number, hence why 39 divided by -3 results in -13.

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91影视

Simplify using the order of operations. $$\left[(-8)^{2}-5^{2}\right] \div(-4+1)$$

Short Answer

Step by step solution

Simplify Exponents

Perform Subtraction Inside the Brackets

Simplify Inside the Parentheses

Perform the Division

Key Concepts

Simplifying Exponents

Performing Arithmetic Operations

Division

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