Simplify The Expression:${6^2 - 4(1)(3)}$Type Your Answer.

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Understanding the Expression

The given expression is $6^2 - 4(1)(3)$. To simplify 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).

Evaluating Exponents

The first step is to evaluate the exponent in the expression. In this case, we have $6^2$, which means $6$ raised to the power of $2$. To evaluate this, we multiply $6$ by itself $2$ times: $6 \times 6 = 36$.

Evaluating Multiplication

Next, we need to evaluate the multiplication in the expression. We have $4(1)(3)$, which means $4$ multiplied by $1$ and then multiplied by $3$. However, since $1$ is a multiplicative identity, we can simplify this to just $4 \times 3 = 12$.

Combining the Results

Now that we have evaluated the exponent and the multiplication, we can combine the results to simplify the expression. We have $36 - 12$, which is a simple subtraction problem.

Final Result

To simplify the expression $6^2 - 4(1)(3)$, we need to follow the order of operations and evaluate the exponent and the multiplication first. Then, we can combine the results to get the final answer.

Step-by-Step Solution

Here's a step-by-step solution to simplify the expression:

1. Evaluate the exponent: $6^2 = 36$
2. Evaluate the multiplication: $4(1)(3) = 12$
3. Combine the results: $36 - 12 = 24$

Conclusion

In conclusion, the simplified expression is $24$. This is the final answer to the given problem.

Additional Tips and Tricks

When simplifying expressions, it's essential to follow the order of operations (PEMDAS) to ensure that you get the correct result. Additionally, make sure to evaluate exponents and multiplication before combining the results.

Common Mistakes to Avoid

When simplifying expressions, some common mistakes to avoid include:

• Not following the order of operations (PEMDAS)
• Not evaluating exponents and multiplication before combining the results
• Not simplifying the expression correctly

Real-World Applications

Simplifying expressions is an essential skill in mathematics, and it has many real-world applications. For example, in physics, you may need to simplify expressions to solve problems involving motion and energy. In engineering, you may need to simplify expressions to design and optimize systems.

Practice Problems

Here are some practice problems to help you improve your skills in simplifying expressions:

• Simplify the expression: $3^2 - 2(1)(4)$
• Simplify the expression: $5^2 - 3(2)(1)$
• Simplify the expression: $2^3 - 4(1)(3)$

Final Thoughts

Simplifying expressions is an essential skill in mathematics, and it has many real-world applications. By following the order of operations (PEMDAS) and evaluating exponents and multiplication before combining the results, you can simplify expressions correctly and accurately.

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Frequently Asked Questions

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. 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 exponents?

A: To evaluate exponents, you need to multiply the base number by itself as many times as the exponent indicates. For example, $6^2$ means $6$ multiplied by itself $2$ times, which is $6 \times 6 = 36$.

Q: How do I evaluate multiplication?

A: To evaluate multiplication, you need to multiply the numbers together. For example, $4(1)(3)$ means $4$ multiplied by $1$ and then multiplied by $3$, which is $4 \times 3 = 12$.

Q: What is the difference between multiplication and addition?

A: Multiplication and addition are two different operations. Multiplication involves multiplying numbers together, while addition involves adding numbers together. For example, $4 \times 3$ is a multiplication problem, while $4 + 3$ is an addition problem.

Q: How do I simplify expressions?

A: To simplify expressions, you need to follow the order of operations (PEMDAS) and evaluate exponents and multiplication before combining the results. For example, to simplify the expression $6^2 - 4(1)(3)$, you need to evaluate the exponent and the multiplication first, and then combine the results.

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

A: Some common mistakes to avoid when simplifying expressions include not following the order of operations (PEMDAS), not evaluating exponents and multiplication before combining the results, and not simplifying the expression correctly.

Q: How do I apply simplifying expressions in real-world situations?

A: Simplifying expressions is an essential skill in mathematics, and it has many real-world applications. For example, in physics, you may need to simplify expressions to solve problems involving motion and energy. In engineering, you may need to simplify expressions to design and optimize systems.

Q: What are some practice problems to help me improve my skills in simplifying expressions?

A: Here are some practice problems to help you improve your skills in simplifying expressions:

• Simplify the expression: $3^2 - 2(1)(4)$
• Simplify the expression: $5^2 - 3(2)(1)$
• Simplify the expression: $2^3 - 4(1)(3)$

Q: How do I know if I have simplified an expression correctly?

A: To know if you have simplified an expression correctly, you need to check your work and make sure that you have followed the order of operations (PEMDAS) and evaluated exponents and multiplication before combining the results.

Q: What are some tips and tricks for simplifying expressions?

A: Here are some tips and tricks for simplifying expressions:

• Make sure to follow the order of operations (PEMDAS)
• Evaluate exponents and multiplication before combining the results
• Simplify the expression correctly
• Check your work to make sure that you have simplified the expression correctly

Conclusion

In conclusion, simplifying expressions is an essential skill in mathematics, and it has many real-world applications. By following the order of operations (PEMDAS) and evaluating exponents and multiplication before combining the results, you can simplify expressions correctly and accurately. Remember to check your work and make sure that you have simplified the expression correctly.