Simplify The Expression:$\[ 6(-4)^8 - 5(-7)^2 - \sqrt{64} + (5) - (14) = \\]

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Introduction

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In this article, we will simplify the given mathematical expression step by step. The expression is: ${ 6(-4)^8 - 5(-7)^2 - \sqrt{64} + (5) - (14) = }$. We will use the order of operations (PEMDAS) to simplify the expression.

Understanding the Order of Operations

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The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:

• Parentheses: Evaluate expressions inside parentheses first.
• Exponents: Evaluate any exponential expressions next (e.g., 2^3).
• Multiplication and Division: Evaluate multiplication and division operations from left to right.
• Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Simplifying the Expression

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Let's start simplifying the expression step by step.

Step 1: Evaluate the Exponents

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The expression contains two exponential expressions: $(-4)^8$ and $(-7)^2$. We will evaluate these expressions first.

• $(-4)^8$ = $(-4) \times (-4) \times (-4) \times (-4) \times (-4) \times (-4) \times (-4) \times (-4)$

• $(-4)^8$ = $256 \times 256 \times 256 \times 256 \times 256 \times 256 \times 256 \times 256$

• $(-4)^8$ = $4294967296$

• $(-7)^2$ = $(-7) \times (-7)$

• $(-7)^2$ = $49$

Step 2: Evaluate the Square Root

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The expression contains a square root: $\sqrt{64}$. We will evaluate this expression next.

• $\sqrt{64}$ = $8$

Step 3: Multiply and Divide

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The expression contains multiplication and division operations. We will evaluate these operations from left to right.

• $6 \times (-4)^8$ = $6 \times 4294967296$
• $6 \times (-4)^8$ = $25749693776$
• $5 \times (-7)^2$ = $5 \times 49$
• $5 \times (-7)^2$ = $245$

Step 4: Add and Subtract

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The expression contains addition and subtraction operations. We will evaluate these operations from left to right.

• $25749693776 - 245$ = $25749693731$
• $25749693731 - 8$ = $25749693723$
• $25749693723 + 5$ = $25749693728$
• $25749693728 - 14$ = $25749693714$

Conclusion

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In this article, we simplified the given mathematical expression step by step using the order of operations (PEMDAS). We evaluated the exponents, square root, multiplication and division operations, and finally, addition and subtraction operations. The simplified expression is: $25749693714$.

Frequently Asked Questions

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Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:

• Parentheses: Evaluate expressions inside parentheses first.
• Exponents: Evaluate any exponential expressions next (e.g., 2^3).
• Multiplication and Division: Evaluate multiplication and division operations from left to right.
• Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify an expression using the order of operations?

A: To simplify an expression using the order of operations, follow these steps:

1. Evaluate any expressions inside parentheses.
2. Evaluate any exponential expressions.
3. Evaluate any multiplication and division operations from left to right.
4. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the difference between multiplication and division?

A: Multiplication and division are both operations that involve numbers, but they have different effects on the numbers. Multiplication involves adding a number a certain number of times, while division involves sharing a number into equal groups.

Q: What is the difference between addition and subtraction?

A: Addition and subtraction are both operations that involve numbers, but they have different effects on the numbers. Addition involves combining two or more numbers, while subtraction involves finding the difference between two numbers.

References

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• Order of Operations (PEMDAS)
• Simplifying Expressions
• Exponents
• Square Roots
• Multiplication and Division
• Addition and Subtraction
  

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Introduction

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In our previous article, we simplified the given mathematical expression step by step using the order of operations (PEMDAS). In this article, we will answer some frequently asked questions related to simplifying expressions and the order of operations.

Q&A

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Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:

• Parentheses: Evaluate expressions inside parentheses first.
• Exponents: Evaluate any exponential expressions next (e.g., 2^3).
• Multiplication and Division: Evaluate multiplication and division operations from left to right.
• Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify an expression using the order of operations?

A: To simplify an expression using the order of operations, follow these steps:

1. Evaluate any expressions inside parentheses.
2. Evaluate any exponential expressions.
3. Evaluate any multiplication and division operations from left to right.
4. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the difference between multiplication and division?

A: Multiplication and division are both operations that involve numbers, but they have different effects on the numbers. Multiplication involves adding a number a certain number of times, while division involves sharing a number into equal groups.

Q: What is the difference between addition and subtraction?

A: Addition and subtraction are both operations that involve numbers, but they have different effects on the numbers. Addition involves combining two or more numbers, while subtraction involves finding the difference between two numbers.

Q: Can I simplify an expression with multiple operations?

A: Yes, you can simplify an expression with multiple operations by following the order of operations. For example, if you have the expression: $2 + 3 \times 4 - 5$, you would first multiply 3 and 4, then add 2 and the result, and finally subtract 5.

Q: How do I handle negative numbers in an expression?

A: When working with negative numbers, remember that a negative number multiplied by a negative number is a positive number, and a negative number added to a negative number is a negative number.

Q: Can I simplify an expression with fractions?

A: Yes, you can simplify an expression with fractions by following the order of operations. For example, if you have the expression: $\frac{1}{2} + \frac{1}{3}$, you would first find a common denominator, then add the fractions.

Q: How do I handle decimals in an expression?

A: When working with decimals, remember that a decimal number multiplied by a decimal number is a decimal number, and a decimal number added to a decimal number is a decimal number.

Tips and Tricks

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Tip 1: Use the Order of Operations

The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. By following the order of operations, you can simplify expressions and avoid errors.

Tip 2: Simplify Expressions Step by Step

Simplifying expressions step by step can help you avoid errors and make the process easier. Start by evaluating any expressions inside parentheses, then evaluate any exponential expressions, and finally evaluate any multiplication and division operations from left to right.

Tip 3: Use Parentheses to Clarify Expressions

Using parentheses to clarify expressions can help you avoid errors and make the process easier. For example, if you have the expression: $2 + 3 \times 4 - 5$, you can use parentheses to clarify the expression: $(2 + 3) \times 4 - 5$.

Conclusion

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In this article, we answered some frequently asked questions related to simplifying expressions and the order of operations. By following the order of operations and simplifying expressions step by step, you can simplify expressions and avoid errors. Remember to use parentheses to clarify expressions and handle negative numbers, fractions, and decimals correctly.

Frequently Asked Questions

---

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:

• Parentheses: Evaluate expressions inside parentheses first.
• Exponents: Evaluate any exponential expressions next (e.g., 2^3).
• Multiplication and Division: Evaluate multiplication and division operations from left to right.
• Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify an expression using the order of operations?

A: To simplify an expression using the order of operations, follow these steps:

1. Evaluate any expressions inside parentheses.
2. Evaluate any exponential expressions.
3. Evaluate any multiplication and division operations from left to right.
4. Finally, evaluate any addition and subtraction operations from left to right.

References

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• Order of Operations (PEMDAS)
• Simplifying Expressions
• Exponents
• Square Roots
• Multiplication and Division
• Addition and Subtraction