Andre Says, I Multiplied 4 By 5, Then Cubed The Result. Select All Expressions That Equal Andre's Answer.A. $(4 \cdot 5)^3$ B. $20^3$ C. 500 D. $4 \cdot 5^3$ E. \$(4 \cdot 5)^2$[/tex\] F. $5^3

Introduction

In mathematics, calculations can be performed in various ways, and understanding the order of operations is crucial to obtaining the correct result. In this article, we will delve into the calculation performed by Andre, who multiplied 4 by 5 and then cubed the result. We will examine each expression given in the options and determine which ones equal Andre's answer.

The Calculation Performed by Andre

Andre's calculation can be broken down into two steps:

1. Multiply 4 by 5: $4 \cdot 5 = 20$
2. Cube the result: $20^3$

Analyzing the Options

Let's analyze each expression given in the options and determine if it equals Andre's answer.

Option A: $(4 \cdot 5)^3$

This expression represents the result of multiplying 4 by 5 and then cubing the result. Using the order of operations, we can evaluate this expression as follows:

$$(4 \cdot 5)^3 = (20)^3 = 8000$$

This expression equals Andre's answer.

Option B: $20^3$

This expression represents the result of cubing 20, which is the same as Andre's calculation. Using the order of operations, we can evaluate this expression as follows:

$$20^3 = 8000$$

This expression equals Andre's answer.

Option C: 500

This expression does not equal Andre's answer. To evaluate this expression, we need to determine what operation was performed to obtain 500. However, without additional information, we cannot determine the correct operation.

Option D: $4 \cdot 5^3$

This expression represents the result of multiplying 4 by the cube of 5. Using the order of operations, we can evaluate this expression as follows:

$$4 \cdot 5^3 = 4 \cdot 125 = 500$$

This expression does not equal Andre's answer.

Option E: $(4 \cdot 5)^2$

This expression represents the result of multiplying 4 by 5 and then squaring the result. Using the order of operations, we can evaluate this expression as follows:

$$(4 \cdot 5)^2 = (20)^2 = 400$$

This expression does not equal Andre's answer.

Option F: $5^3$

This expression represents the result of cubing 5. Using the order of operations, we can evaluate this expression as follows:

$$5^3 = 125$$

This expression does not equal Andre's answer.

Conclusion

In conclusion, the expressions that equal Andre's answer are:

• $$(4 \cdot 5)^3$$

• $$20^3$$

These expressions represent the result of multiplying 4 by 5 and then cubing the result, which is the same as Andre's calculation. The other options do not equal Andre's answer.

Recommendations

When performing calculations, it is essential to follow the order of operations to ensure that the correct result is obtained. In this case, Andre's calculation can be broken down into two steps: multiplying 4 by 5 and then cubing the result. By following the order of operations, we can determine which expressions equal Andre's answer.

Final Thoughts

Introduction

In our previous article, we explored Andre's calculation, who multiplied 4 by 5 and then cubed the result. We analyzed each expression given in the options and determined which ones equal Andre's answer. In this article, we will provide a Q&A section to further clarify any doubts and provide additional insights into the calculation.

Q&A

Q: What is the order of operations?

A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed. The order of operations is often remembered using the acronym PEMDAS, which stands for:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
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: How do I evaluate the expression $(4 \cdot 5)^3$?

A: To evaluate the expression $(4 \cdot 5)^3$, you need to follow the order of operations. First, multiply 4 by 5 to get 20. Then, cube the result by raising it to the power of 3.

$$(4 \cdot 5)^3 = (20)^3 = 8000$$

Q: What is the difference between $(4 \cdot 5)^3$ and $20^3$?

A: The expressions $(4 \cdot 5)^3$ and $20^3$ are equivalent, but they are written in different ways. The expression $(4 \cdot 5)^3$ represents the result of multiplying 4 by 5 and then cubing the result, while the expression $20^3$ represents the result of cubing 20 directly.

Q: How do I determine which expressions equal Andre's answer?

A: To determine which expressions equal Andre's answer, you need to evaluate each expression using the order of operations. If the result of the expression is equal to 8000, then it equals Andre's answer.

Q: What is the significance of the order of operations in mathematics?

A: The order of operations is crucial in mathematics because it ensures that mathematical expressions are evaluated consistently and accurately. Without the order of operations, mathematical expressions could be evaluated differently depending on the order in which they are performed.

Q: Can you provide more examples of expressions that equal Andre's answer?

A: Yes, here are a few more examples of expressions that equal Andre's answer:

• $$(4 \cdot 5)^3$$

• $$20^3$$

• $$(4 \cdot (5^3))$$

• $$(4 \cdot 5) \cdot 5^2$$

These expressions all represent the result of multiplying 4 by 5 and then cubing the result.

Conclusion

In conclusion, the Q&A section provides additional insights into Andre's calculation and the order of operations. By following the order of operations, we can evaluate mathematical expressions consistently and accurately. We hope this article has been helpful in clarifying any doubts and providing a deeper understanding of the calculation performed by Andre.

Recommendations

When performing calculations, it is essential to follow the order of operations to ensure that the correct result is obtained. By following the order of operations, we can determine which expressions equal Andre's answer and ensure that mathematical expressions are evaluated consistently and accurately.

Final Thoughts

In mathematics, calculations can be performed in various ways, and understanding the order of operations is crucial to obtaining the correct result. By analyzing each expression given in the options and following the order of operations, we can determine which expressions equal Andre's answer. This article provides a Q&A section to further clarify any doubts and provide additional insights into the calculation.