Evaluate The Expression:a. $3.2^2\left(11.6^2+7.8^3\right$\]

Introduction

In this article, we will evaluate the given mathematical expression: $3.2^2\left(11.6^2+7.8^3\right)$. This expression involves exponentiation, addition, and multiplication operations. We will break down the expression into smaller parts, evaluate each part, and then combine the results to obtain the final answer.

Step 1: Evaluate the Exponents

The expression contains two exponentiation operations: $3.2^2$ and $11.6^2$. We will start by evaluating these exponents.

• $3.2^2 = 3.2 \times 3.2 = 10.24$
• $11.6^2 = 11.6 \times 11.6 = 134.56$

Step 2: Evaluate the Cubic Expression

The expression also contains a cubic operation: $7.8^3$. We will evaluate this operation next.

• $7.8^3 = 7.8 \times 7.8 \times 7.8 = 4744.088$

Step 3: Add the Results of the Exponents and the Cubic Expression

Now that we have evaluated the exponents and the cubic expression, we can add the results.

• $11.6^2 + 7.8^3 = 134.56 + 4744.088 = 4878.648$

Step 4: Multiply the Results by 3.2^2

The final step is to multiply the result of the addition by $3.2^2$.

• $3.2^2 \times (11.6^2 + 7.8^3) = 10.24 \times 4878.648 = 49891.9424$

Conclusion

In this article, we evaluated the given mathematical expression: $3.2^2\left(11.6^2+7.8^3\right)$. We broke down the expression into smaller parts, evaluated each part, and then combined the results to obtain the final answer. The final result is $49891.9424$.

Key Takeaways

• Exponentiation operations should be evaluated first.
• Cubic operations should be evaluated next.
• Addition and multiplication operations should be performed in the order they appear in the expression.
• The final result should be obtained by combining the results of the previous steps.

Real-World Applications

Evaluating mathematical expressions like the one in this article has many real-world applications. For example, in engineering, scientists, and economists, mathematical expressions are used to model and analyze complex systems. In finance, mathematical expressions are used to calculate interest rates, investment returns, and other financial metrics. In computer science, mathematical expressions are used to optimize algorithms and solve complex problems.

Common Mistakes to Avoid

When evaluating mathematical expressions, there are several common mistakes to avoid. These include:

• Evaluating addition and multiplication operations in the wrong order.
• Forgetting to evaluate exponentiation operations.
• Not following the order of operations (PEMDAS).
• Not checking the units of the variables in the expression.

Conclusion

Introduction

In our previous article, we evaluated the mathematical expression: $3.2^2\left(11.6^2+7.8^3\right)$. We broke down the expression into smaller parts, evaluated each part, and then combined the results to obtain the final answer. In this article, we will answer some frequently asked questions about evaluating mathematical expressions like the one in this article.

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 a mathematical expression. The order of operations is:

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: Why is it important to follow the order of operations?

A: Following the order of operations is important because it ensures that mathematical expressions are evaluated consistently and accurately. If we don't follow the order of operations, we may get different results depending on the order in which we evaluate the operations.

Q: How do I evaluate exponential expressions?

A: To evaluate exponential expressions, we need to multiply the base number by itself as many times as the exponent indicates. For example, to evaluate $2^3$, we would multiply 2 by itself three times: $2 \times 2 \times 2 = 8$.

Q: What is the difference between a cubic expression and an exponential expression?

A: A cubic expression is an expression that involves the product of three numbers, one of which is raised to the power of 3. For example, $2 \times 3 \times 4$ is a cubic expression. An exponential expression, on the other hand, is an expression that involves a number raised to a power. For example, $2^3$ is an exponential expression.

Q: How do I evaluate expressions with multiple operations?

A: To evaluate expressions with multiple operations, we need to follow the order of operations. We start by evaluating any expressions inside parentheses, then any exponential expressions, and so on. We continue evaluating the operations in the order they appear in the expression until we have evaluated all the operations.

Q: What are some common mistakes to avoid when evaluating mathematical expressions?

A: Some common mistakes to avoid when evaluating mathematical expressions include:

• Evaluating addition and multiplication operations in the wrong order.
• Forgetting to evaluate exponentiation operations.
• Not following the order of operations (PEMDAS).
• Not checking the units of the variables in the expression.

Q: How can I practice evaluating mathematical expressions?

A: There are many ways to practice evaluating mathematical expressions. You can start by working through simple expressions and gradually move on to more complex ones. You can also use online resources, such as calculators and math websites, to practice evaluating expressions. Additionally, you can work with a tutor or teacher to get help with evaluating expressions.

Conclusion

In conclusion, evaluating mathematical expressions like the one in this article requires careful attention to the order of operations and the evaluation of exponentiation, addition, and multiplication operations. By following the steps outlined in this article and avoiding common mistakes, you can ensure that you obtain the correct result.