Evaluate $4 + (m-n)^4$ When $m = 7$ And \$n = 5$[/tex\].The Value Of The Expression Is:

Introduction

In this article, we will evaluate the expression $4 + (m-n)^4$ when $m = 7$ and $n = 5$. This involves substituting the given values of $m$ and $n$ into the expression and simplifying it to obtain the final value.

Understanding the Expression

The given expression is $4 + (m-n)^4$. This expression involves the subtraction of $n$ from $m$, raising the result to the power of $4$, and then adding $4$ to it. To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate the expression inside the parentheses.
2. Exponents: Raise the result to the power of $4$.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Substituting the Values of $m$ and $n$

We are given that $m = 7$ and $n = 5$. We will substitute these values into the expression $4 + (m-n)^4$.

$$4 + (7-5)^4$$

Evaluating the Expression Inside the Parentheses

The expression inside the parentheses is $7-5$. We will evaluate this expression first.

$$7-5 = 2$$

Substituting the Result Back into the Original Expression

Now that we have evaluated the expression inside the parentheses, we will substitute the result back into the original expression.

$$4 + (2)^4$$

Evaluating the Exponent

The exponent is $4$. We will raise $2$ to the power of $4$.

$$2^4 = 16$$

Substituting the Result Back into the Original Expression

Now that we have evaluated the exponent, we will substitute the result back into the original expression.

$$4 + 16$$

Evaluating the Final Expression

The final expression is $4 + 16$. We will evaluate this expression by adding $4$ and $16$.

$$4 + 16 = 20$$

Conclusion

In this article, we evaluated the expression $4 + (m-n)^4$ when $m = 7$ and $n = 5$. We followed the order of operations (PEMDAS) and substituted the given values of $m$ and $n$ into the expression. The final value of the expression is $20$.

Frequently Asked Questions

• What is the value of the expression $4 + (m-n)^4$ when $m = 7$ and $n = 5$?
• How do we evaluate the expression $4 + (m-n)^4$ when $m = 7$ and $n = 5$?
• What is the order of operations (PEMDAS) and how do we use it to evaluate expressions?

Final Answer

The final answer is $20$.

Introduction

In our previous article, we evaluated the expression $4 + (m-n)^4$ when $m = 7$ and $n = 5$. We followed the order of operations (PEMDAS) and substituted the given values of $m$ and $n$ into the expression. In this article, we will answer some frequently asked questions related to evaluating the expression $4 + (m-n)^4$.

Q&A

Q: What is the value of the expression $4 + (m-n)^4$ when $m = 7$ and $n = 5$?

A: The value of the expression $4 + (m-n)^4$ when $m = 7$ and $n = 5$ is $20$.

Q: How do we evaluate the expression $4 + (m-n)^4$ when $m = 7$ and $n = 5$?

A: To evaluate the expression $4 + (m-n)^4$ when $m = 7$ and $n = 5$, we need to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate the expression inside the parentheses.
2. Exponents: Raise the result to the power of $4$.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the order of operations (PEMDAS) and how do we use it to evaluate expressions?

A: The order of operations (PEMDAS) 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 the expression inside the parentheses.
• Exponents: Raise the result to the power of the exponent.
• Multiplication and Division: Evaluate any 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 we handle negative numbers when evaluating expressions?

A: When evaluating expressions, we need to handle negative numbers carefully. For example, if we have the expression $-3^2$, we need to evaluate the exponent first and then multiply the result by $-1$.

Q: Can we use the order of operations (PEMDAS) to evaluate expressions with fractions?

A: Yes, we can use the order of operations (PEMDAS) to evaluate expressions with fractions. For example, if we have the expression $\frac{1}{2} + \frac{1}{3}$, we need to follow the order of operations (PEMDAS) to evaluate the expression.

Q: How do we evaluate expressions with variables?

A: When evaluating expressions with variables, we need to follow the order of operations (PEMDAS) and substitute the values of the variables into the expression.

Conclusion

In this article, we answered some frequently asked questions related to evaluating the expression $4 + (m-n)^4$. We discussed the order of operations (PEMDAS) and how to use it to evaluate expressions with variables, fractions, and negative numbers.

Frequently Asked Questions

• How do we evaluate expressions with variables?
• Can we use the order of operations (PEMDAS) to evaluate expressions with fractions?
• How do we handle negative numbers when evaluating expressions?
• What is the order of operations (PEMDAS) and how do we use it to evaluate expressions?

Final Answer

The final answer is $20$.