What Value Is Equivalent To This Expression?$4^2 - 6(7 - 10$\]A. 7 B. -12 C. 34 D. -36

Introduction

In mathematics, expressions are used to represent a value or a relationship between values. Evaluating an expression involves simplifying it to a single value. In this article, we will focus on evaluating the expression $4^2 - 6(7 - 10)$ and determining its equivalent value.

Understanding the Expression

The given expression is $4^2 - 6(7 - 10)$. To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate the expressions inside the parentheses.
2. Exponents: Evaluate any exponential expressions.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

Evaluating the Expression

Let's start by evaluating the expression inside the parentheses: $7 - 10$. This expression is equal to $-3$.

Now, we can rewrite the original expression as $4^2 - 6(-3)$.

Evaluating Exponents

Next, we need to evaluate the exponential expression $4^2$. This expression is equal to $16$.

Evaluating Multiplication and Division

Now, we can rewrite the expression as $16 - 6(-3)$.

Evaluating Multiplication

To evaluate the multiplication operation, we need to multiply $6$ by $-3$. This operation is equal to $-18$.

Evaluating Addition and Subtraction

Finally, we can evaluate the addition and subtraction operations. We have $16 - (-18)$. To subtract a negative number, we can add its positive counterpart. Therefore, this expression is equal to $16 + 18$.

Final Evaluation

The final evaluation of the expression $4^2 - 6(7 - 10)$ is $16 + 18$, which is equal to $34$.

Conclusion

In this article, we evaluated the expression $4^2 - 6(7 - 10)$ and determined its equivalent value. By following the order of operations and simplifying the expression, we found that the equivalent value is $34$.

Frequently Asked Questions

• What is the order of operations? The order of operations is a set of rules that tells us which operations to perform first when evaluating an expression. The order of operations is:
  1. Parentheses
  2. Exponents
  3. Multiplication and Division
  4. Addition and Subtraction
• How do I evaluate an expression with parentheses? To evaluate an expression with parentheses, we need to evaluate the expressions inside the parentheses first. Then, we can evaluate the rest of the expression.
• What is the difference between $-3$ and $-(-3)$? The expression $-(-3)$ is equal to $3$, not $-3$. This is because subtracting a negative number is the same as adding its positive counterpart.

Final Answer

The final answer is $\boxed{34}$.

Introduction

Evaluating expressions is a fundamental concept in mathematics. In our previous article, we evaluated the expression $4^2 - 6(7 - 10)$ and determined its equivalent value. In this article, we will answer some frequently asked questions about evaluating expressions.

Q&A

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 evaluating an expression. The order of operations is: 1. Parentheses 2. Exponents 3. Multiplication and Division 4. Addition and Subtraction

Q: How do I evaluate an expression with parentheses?

A: To evaluate an expression with parentheses, we need to evaluate the expressions inside the parentheses first. Then, we can evaluate the rest of the expression.

Q: What is the difference between $-3$ and $-(-3)$?

A: The expression $-(-3)$ is equal to $3$, not $-3$. This is because subtracting a negative number is the same as adding its positive counterpart.

Q: How do I evaluate an expression with multiple operations?

A: To evaluate an expression with multiple operations, we need to follow the order of operations. We start by evaluating the expressions inside the parentheses, then we evaluate any exponential expressions, followed by any multiplication and division operations, and finally any addition and subtraction operations.

Q: What is the difference between $2^3$ and $2 \times 2 \times 2$?

A: The expressions $2^3$ and $2 \times 2 \times 2$ are equal. The exponentiation operation $2^3$ is equivalent to multiplying $2$ by itself three times.

Q: How do I evaluate an expression with variables?

A: To evaluate an expression with variables, we need to substitute the values of the variables into the expression. For example, if we have the expression $x + 2$, and we know that $x = 3$, we can substitute $x$ with $3$ to get $3 + 2$.

Q: What is the difference between $-5 + 3$ and $-5 - 3$?

A: The expressions $-5 + 3$ and $-5 - 3$ are not equal. The expression $-5 + 3$ is equal to $-2$, while the expression $-5 - 3$ is equal to $-8$.

Q: How do I evaluate an expression with fractions?

A: To evaluate an expression with fractions, we need to follow the order of operations. We start by evaluating any exponential expressions, followed by any multiplication and division operations, and finally any addition and subtraction operations.

Q: What is the difference between $\frac{1}{2} + \frac{1}{4}$ and $\frac{1}{2} - \frac{1}{4}$?

A: The expressions $\frac{1}{2} + \frac{1}{4}$ and $\frac{1}{2} - \frac{1}{4}$ are not equal. The expression $\frac{1}{2} + \frac{1}{4}$ is equal to $\frac{3}{4}$, while the expression $\frac{1}{2} - \frac{1}{4}$ is equal to $\frac{1}{4}$.

Conclusion

Evaluating expressions is a fundamental concept in mathematics. By following the order of operations and simplifying expressions, we can determine their equivalent values. In this article, we answered some frequently asked questions about evaluating expressions.

Final Answer

The final answer is $\boxed{34}$.