Simplify The Expression: ( ( 4 3 ) 2 X ) 1 \left(\left(\frac{4}{3}\right)^2 X\right)^1 ( ( 3 4 ​ ) 2 X ) 1 A. 16 3 X 2 \frac{16}{3} X^2 3 16 ​ X 2 B. 64 27 X \frac{64}{27} X 27 64 ​ X C. 64 27 X 2 \frac{64}{27} X^2 27 64 ​ X 2 D. 16 9 X \frac{16}{9} X 9 16 ​ X Please Select The Best Answer From The Choices

Introduction

Exponential expressions can be complex and intimidating, but with a clear understanding of the rules and procedures, they can be simplified with ease. In this article, we will focus on simplifying the expression $\left(\left(\frac{4}{3}\right)^2 x\right)^1$ using the properties of exponents. We will explore the different options available and determine the correct answer.

Understanding Exponents

Exponents are a shorthand way of representing repeated multiplication. For example, $a^2$ means $a \times a$, and $a^3$ means $a \times a \times a$. When we have an expression with multiple exponents, we can simplify it by applying the rules of exponents.

Simplifying the Expression

Let's start by simplifying the expression $\left(\left(\frac{4}{3}\right)^2 x\right)^1$. To do this, we need to apply the rule of exponents that states $(a^m)^n = a^{m \times n}$.

\left(\left(\frac{4}{3}\right)^2 x\right)^1 = \left(\frac{4}{3}\right)^{2 \times 1} x^1

Now, we can simplify the expression further by applying the rule of exponents that states $a^m \times a^n = a^{m + n}$.

\left(\frac{4}{3}\right)^{2 \times 1} x^1 = \left(\frac{4}{3}\right)^2 x

Next, we can simplify the expression $\left(\frac{4}{3}\right)^2$ by applying the rule of exponents that states $(a/b)^m = (a^m)/(b^m)$.

\left(\frac{4}{3}\right)^2 = \frac{4^2}{3^2} = \frac{16}{9}

Now, we can substitute this value back into the expression.

\frac{16}{9} x

Evaluating the Options

Now that we have simplified the expression, let's evaluate the options available.

• Option a: $\frac{16}{3} x^2$
• Option b: $\frac{64}{27} x$
• Option c: $\frac{64}{27} x^2$
• Option d: $\frac{16}{9} x$

Based on our simplification, we can see that the correct answer is option d: $\frac{16}{9} x$.

Conclusion

Simplifying exponential expressions can be a complex task, but with a clear understanding of the rules and procedures, it can be done with ease. In this article, we simplified the expression $\left(\left(\frac{4}{3}\right)^2 x\right)^1$ using the properties of exponents and determined the correct answer. We hope that this article has provided you with a better understanding of how to simplify exponential expressions and has helped you to develop your problem-solving skills.

Common Mistakes to Avoid

When simplifying exponential expressions, there are several common mistakes to avoid.

• Not applying the rules of exponents: Make sure to apply the rules of exponents correctly to simplify the expression.
• Not simplifying the expression fully: Make sure to simplify the expression fully by applying all the rules of exponents.
• Not checking the options: Make sure to check the options available and choose the correct answer.

Practice Problems

To practice simplifying exponential expressions, try the following problems.

• Simplify the expression $\left(\left(\frac{2}{3}\right)^3 x\right)^2$.
• Simplify the expression $\left(\left(\frac{3}{4}\right)^2 x\right)^3$.
• Simplify the expression $\left(\left(\frac{5}{6}\right)^4 x\right)^1$.

Final Thoughts

Introduction

In our previous article, we explored the concept of simplifying exponential expressions and provided a step-by-step guide on how to simplify the expression $\left(\left(\frac{4}{3}\right)^2 x\right)^1$. In this article, we will provide a Q&A guide to help you better understand the concept and provide additional practice problems to help you develop your skills.

Q&A

Q: What is the rule of exponents that states $(a^m)^n = a^{m \times n}$?

A: This rule states that when we have an expression with multiple exponents, we can simplify it by multiplying the exponents.

Q: How do we simplify the expression $\left(\left(\frac{4}{3}\right)^2 x\right)^1$?

A: To simplify this expression, we need to apply the rule of exponents that states $(a^m)^n = a^{m \times n}$. We can then simplify the expression further by applying the rule of exponents that states $a^m \times a^n = a^{m + n}$.

Q: What is the correct answer for the expression $\left(\left(\frac{4}{3}\right)^2 x\right)^1$?

A: The correct answer is $\frac{16}{9} x$.

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

A: Some common mistakes to avoid include not applying the rules of exponents, not simplifying the expression fully, and not checking the options available.

Q: How can I practice simplifying exponential expressions?

A: You can practice simplifying exponential expressions by trying the following problems:

• Simplify the expression $\left(\left(\frac{2}{3}\right)^3 x\right)^2$.
• Simplify the expression $\left(\left(\frac{3}{4}\right)^2 x\right)^3$.
• Simplify the expression $\left(\left(\frac{5}{6}\right)^4 x\right)^1$.

Q: What are some additional tips for simplifying exponential expressions?

A: Some additional tips for simplifying exponential expressions include:

• Make sure to apply the rules of exponents correctly.
• Simplify the expression fully by applying all the rules of exponents.
• Check the options available and choose the correct answer.

Practice Problems

To practice simplifying exponential expressions, try the following problems.

• Simplify the expression $\left(\left(\frac{2}{3}\right)^3 x\right)^2$.
• Simplify the expression $\left(\left(\frac{3}{4}\right)^2 x\right)^3$.
• Simplify the expression $\left(\left(\frac{5}{6}\right)^4 x\right)^1$.

Answer Key

• $\left(\left(\frac{2}{3}\right)^3 x\right)^2 = \frac{8}{27} x^2$
• $\left(\left(\frac{3}{4}\right)^2 x\right)^3 = \frac{27}{64} x^3$
• \left(\left(\frac{5}{6}\right4 x\right)^1 = \frac{625}{1296} x

Conclusion

Simplifying exponential expressions is an important skill to develop, and with practice, you can become proficient in simplifying even the most complex expressions. Remember to apply the rules of exponents correctly, simplify the expression fully, and check the options available. With these tips and practice problems, you will be well on your way to becoming an expert in simplifying exponential expressions.

Additional Resources

For additional resources on simplifying exponential expressions, try the following:

• Khan Academy: Exponents and Exponential Functions
• Mathway: Exponents and Exponential Functions
• Wolfram Alpha: Exponents and Exponential Functions

Final Thoughts

Simplifying exponential expressions is a complex task, but with practice and patience, you can become proficient in simplifying even the most complex expressions. Remember to apply the rules of exponents correctly, simplify the expression fully, and check the options available. With these tips and practice problems, you will be well on your way to becoming an expert in simplifying exponential expressions.