Evaluate The Expression $6^2-(8-4)^2+7$.$6^2-(8-4)^2+7=$

Feb 28, 2025 by ADMIN 57 views

Understanding the Expression

The given expression is $6^2-(8-4)^2+7$ . To evaluate this expression, we need to follow the order of operations (PEMDAS), which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Breaking Down the Expression

Let's break down the expression into smaller parts and evaluate each part step by step.

Evaluating the Exponents

The first part of the expression is $6^2$ . This means we need to raise 6 to the power of 2.

Raising 6 to the Power of 2

$6^2 = 6 \times 6 = 36$

So, the first part of the expression is equal to 36.

Evaluating the Expression Inside the Parentheses

The next part of the expression is $(8-4)^2$ . This means we need to evaluate the expression inside the parentheses first.

Evaluating the Expression Inside the Parentheses

$8-4 = 4$

Now, we need to raise 4 to the power of 2.

Raising 4 to the Power of 2

$4^2 = 4 \times 4 = 16$

So, the expression inside the parentheses is equal to 16.

Combining the Results

Now that we have evaluated the exponents and the expression inside the parentheses, we can combine the results.

Combining the Results

$6^2-(8-4)^2+7 = 36-16+7$

Evaluating the Final Expression

Now that we have combined the results, we can evaluate the final expression.

Evaluating the Final Expression

$36-16+7 = 27$

Therefore, the final answer is 27.

Conclusion

In this article, we evaluated the expression $6^2-(8-4)^2+7$ step by step. We followed the order of operations (PEMDAS) and broke down the expression into smaller parts. We evaluated each part separately and combined the results to get the final answer. The final answer is 27.

Frequently Asked Questions

What is the order of operations (PEMDAS)? 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, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
How do I evaluate an expression with exponents? To evaluate an expression with exponents, we need to raise the base number to the power of the exponent. For example, $6^2$ means we need to raise 6 to the power of 2.
How do I evaluate an expression with parentheses? To evaluate an expression with parentheses, we need to evaluate the expression inside the parentheses first. For example, $(8-4)^2$ means we need to evaluate the expression inside the parentheses first and then raise the result to the power of 2.

Q&A: Evaluating Expressions

Q: What is the order of operations (PEMDAS)?

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, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Q: How do I evaluate an expression with exponents?

A: To evaluate an expression with exponents, we need to raise the base number to the power of the exponent. For example, $6^2$ means we need to raise 6 to the power of 2.

Q: How do I evaluate an expression with parentheses?

A: To evaluate an expression with parentheses, we need to evaluate the expression inside the parentheses first. For example, $(8-4)^2$ means we need to evaluate the expression inside the parentheses first and then raise the result to the power of 2.

Q: What is the difference between multiplication and division?

A: Multiplication and division are both operations that involve numbers, but they have different rules. Multiplication is represented by the symbol $\times$ or $\cdot$ , and it means to add a number a certain number of times. Division is represented by the symbol $\div$ , and it means to find the result of a number being divided by another number.

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 (PEMDAS). We need to evaluate the expressions inside the parentheses first, then the exponents, and finally the multiplication and division operations from left to right. After that, we can perform the addition and subtraction operations from left to right.

Q: What is the rule for evaluating expressions with negative numbers?

A: When evaluating expressions with negative numbers, we need to remember that a negative number multiplied by a negative number is a positive number. For example, $(-3) \times (-4) = 12$ . We also need to remember that a negative number divided by a negative number is a positive number. For example, $(-3) \div (-4) = 0.75$ .

Q: How do I evaluate an expression with a variable?

A: To evaluate an expression with a variable, we need to substitute the value of the variable into the expression. For example, if we have the expression $2x + 3$ and the value of $x$ is 4, we can substitute 4 into the expression to get $2(4) + 3 = 11$ .

Q: What is the rule for evaluating expressions with fractions?

A: When evaluating expressions with fractions, we need to remember that a fraction is a way of representing a part of a whole. We can add and subtract fractions by finding a common denominator and then adding or subtracting the numerators. We can also multiply and divide fractions by multiplying or dividing the numerators and denominators.

Q: How do I evaluate an expression with a decimal?

A: To evaluate an expression with a decimal, we need to follow the same rules as for evaluating expressions with fractions. We can add and subtract decimals by lining up the decimal points and then adding or subtracting the numbers. We can also multiply and divide decimals by multiplying or dividing the numbers and then rounding the result to the correct number of decimal places.