Additional Tips and Resources

Oct 13, 2025 by wbrum.org 134 views

**The First Step in a Problem: Understanding Exponents and Parentheses**

What is the Correct Placement of Parentheses in the Given Expression?

The given expression is $20^{\text{B}} - 3 + 4^{\circ}$ . To determine the correct placement of parentheses, we need to understand the order of operations and the rules of exponents.

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 order of operations is:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
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: What are Exponents?

A: Exponents are a shorthand way of writing repeated multiplication. For example, $2^3$ means $2 \times 2 \times 2$ , which is equal to 8.

Q: How Do We Evaluate Exponents in the Given Expression?

A: In the given expression, $20^{\text{B}}$ and $4^{\circ}$ are both exponential expressions. To evaluate these expressions, we need to understand the rules of exponents.

Q: What are the Rules of Exponents?

A: The rules of exponents are:

Product of Powers: When we multiply two exponential expressions with the same base, we add the exponents. For example, $2^3 \times 2^4 = 2^{3+4} = 2^7$ .
Power of a Power: When we raise an exponential expression to a power, we multiply the exponents. For example, $(2^3)^4 = 2^{3 \times 4} = 2^{12}$ .
Quotient of Powers: When we divide two exponential expressions with the same base, we subtract the exponents. For example, $\frac{2^5}{2^3} = 2^{5-3} = 2^2$ .

Q: How Do We Apply the Rules of Exponents to the Given Expression?

A: In the given expression, $20^{\text{B}}$ and $4^{\circ}$ are both exponential expressions. To evaluate these expressions, we need to apply the rules of exponents.

Q: What is the Correct Placement of Parentheses in the Given Expression?

A: Based on the order of operations and the rules of exponents, the correct placement of parentheses in the given expression is:

$20^{\text{B}} - 3 + 4^{\circ}$

becomes

$20^{\text{B}} - (3 + 4^{\circ})$

$(20^{\text{B}} - 3) + 4^{\circ}$

Q: Why is the Correct Placement of Parentheses Important?

A: The correct placement of parentheses is important because it affects the order of operations and the final result of the expression. If we don't place the parentheses correctly, we may get an incorrect result.

Q: What are the Two Letters that Show Where the Parentheses Should be Placed?

A: The two letters that show where the parentheses should be placed are "B" and "°". These letters indicate the base and exponent of the exponential expressions, respectively.

Conclusion

In conclusion, the correct placement of parentheses in the given expression is important because it affects the order of operations and the final result of the expression. By understanding the order of operations and the rules of exponents, we can determine the correct placement of parentheses and evaluate the expression correctly.

Additional Tips and Resources

For more information on the order of operations, see the Khan Academy video on the order of operations.
For more information on the rules of exponents, see the Khan Academy video on the rules of exponents.
Practice evaluating expressions with exponents and parentheses to improve your skills.

Common Mistakes to Avoid

Not following the order of operations correctly.
Not applying the rules of exponents correctly.
Not placing parentheses correctly.

Real-World Applications

Evaluating expressions with exponents and parentheses is an important skill in many real-world applications, such as science, engineering, and finance.
Understanding the order of operations and the rules of exponents is crucial in many fields, such as physics, chemistry, and mathematics.

Final Thoughts