Match The Expression To The Method Needed To Evaluate. ( 7 2 ) 3 \left(7^2\right)^3 ( 7 2 ) 3

Introduction

Exponential expressions are a fundamental concept in mathematics, and understanding how to evaluate them is crucial for solving various mathematical problems. In this article, we will focus on evaluating the expression $\left(7^2\right)^3$ using the correct method.

Understanding Exponential Expressions

Exponential expressions are written in the form $a^b$, where $a$ is the base and $b$ is the exponent. The base is the number being raised to a power, and the exponent is the power to which the base is being raised. For example, in the expression $2^3$, the base is $2$ and the exponent is $3$.

The Order of Operations

When evaluating exponential expressions, it's essential to follow the order of operations, which 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.

Evaluating $\left(7^2\right)^3$

To evaluate the expression $\left(7^2\right)^3$, we need to follow the order of operations. First, we need to evaluate the expression inside the parentheses, which is $7^2$. This means that we need to raise $7$ to the power of $2$.

Using the Power Rule

The power rule states that when we raise a power to another power, we multiply the exponents. In this case, we have $\left(7^2\right)^3$, which means that we need to multiply the exponent $2$ by the exponent $3$.

$\left(7^2\right)^3 = 7^{2 \times 3} = 7^6$

Evaluating $7^6$

Now that we have simplified the expression to $7^6$, we can evaluate it by raising $7$ to the power of $6$.

$7^6 = 7 \times 7 \times 7 \times 7 \times 7 \times 7 = 117649$

Conclusion

In conclusion, to evaluate the expression $\left(7^2\right)^3$, we need to follow the order of operations and use the power rule to simplify the expression. By raising $7$ to the power of $6$, we can evaluate the expression and find the final answer.

Common Mistakes to Avoid

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

• Not following the order of operations: Failing to follow the order of operations can lead to incorrect answers.
• Not using the power rule: Failing to use the power rule can make it difficult to simplify exponential expressions.
• Not evaluating expressions inside parentheses first: Failing to evaluate expressions inside parentheses first can lead to incorrect answers.

Tips for Evaluating Exponential Expressions

Here are some tips for evaluating exponential expressions:

• Use the power rule: The power rule is a powerful tool for simplifying exponential expressions.
• Follow the order of operations: Failing to follow the order of operations can lead to incorrect answers.
• Evaluate expressions inside parentheses first: Evaluating expressions inside parentheses first can help to simplify the expression and avoid errors.
• Use a calculator: If you're having trouble evaluating an exponential expression, consider using a calculator to help you find the answer.

Practice Problems

Here are some practice problems to help you evaluate exponential expressions:

• $\left(3^4\right)^2$
• $\left(2^5\right)^3$
• $\left(4^3\right)^2$

Answer Key

Here are the answers to the practice problems:

• $\left(3^4\right)^2 = 3^{4 \times 2} = 3^8 = 6561$
• $\left(2^5\right)^3 = 2^{5 \times 3} = 2^{15} = 32768$
• $\left(4^3\right)^2 = 4^{3 \times 2} = 4^6 = 4096$

Conclusion

Introduction

In our previous article, we discussed how to evaluate exponential expressions using the correct method. In this article, we will provide a Q&A guide to help you better understand how to evaluate exponential expressions.

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 an exponential expression?

A: To evaluate an exponential expression, you need to follow the order of operations. First, evaluate any expressions inside parentheses. Then, evaluate any exponential expressions. Finally, evaluate any multiplication and division operations from left to right, and then any addition and subtraction operations from left to right.

Q: What is the power rule?

A: The power rule states that when we raise a power to another power, we multiply the exponents. For example, $\left(7^2\right)^3 = 7^{2 \times 3} = 7^6$.

Q: How do I use the power rule?

A: To use the power rule, you need to multiply the exponents. For example, if you have the expression $\left(7^2\right)^3$, you would multiply the exponent $2$ by the exponent $3$ to get $7^6$.

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

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

• Not following the order of operations: Failing to follow the order of operations can lead to incorrect answers.
• Not using the power rule: Failing to use the power rule can make it difficult to simplify exponential expressions.
• Not evaluating expressions inside parentheses first: Failing to evaluate expressions inside parentheses first can lead to incorrect answers.

Q: How can I practice evaluating exponential expressions?

A: You can practice evaluating exponential expressions by working through practice problems. Here are some practice problems to get you started:

• $\left(3^4\right)^2$
• $\left(2^5\right)^3$
• $\left(4^3\right)^2$

Q: What are some tips for evaluating exponential expressions?

A: Here are some tips for evaluating exponential expressions:

• Use the power rule: The power rule is a powerful tool for simplifying exponential expressions.
• Follow the order of operations: Failing to follow the order of operations can lead to incorrect answers.
• Evaluate expressions inside parentheses first: Evaluating expressions inside parentheses first can help to simplify the expression and avoid errors.
• Use a calculator: If you're having trouble evaluating an exponential expression, consider using a calculator to help you find the answer.

Q: How can I use a calculator to evaluate exponential expressions?

A: To use a calculator to evaluate an exponential expression, simply enter the expression into the calculator and press the "enter" or "=" button. The calculator will then evaluate the expression and display the answer.

Conclusion

In conclusion, evaluating exponential expressions is a crucial skill for solving mathematical problems. By following the order of operations and using the power rule, we can simplify exponential expressions and find the final answer. Remember to avoid common mistakes and use a calculator if you're having trouble evaluating an exponential expression. With practice, you'll become more confident in your ability to evaluate exponential expressions and solve mathematical problems.

Practice Problems

Here are some practice problems to help you evaluate exponential expressions:

• $\left(5^3\right)^2$
• $\left(2^4\right)^3$
• $\left(3^5\right)^2$

Answer Key

Here are the answers to the practice problems:

• $\left(5^3\right)^2 = 5^{3 \times 2} = 5^6 = 15625$
• $\left(2^4\right)^3 = 2^{4 \times 3} = 2^{12} = 4096$
• $\left(3^5\right)^2 = 3^{5 \times 2} = 3^{10} = 59049$