Simplify The Expression $\left(5 A^2 B^3 C^4\right)^4\left(6 A^3 B^4 C^2\right$\]. Write The Variables In Alphabetical Order.

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Introduction

In this article, we will simplify the given expression (5a2b3c4)4(6a3b4c2)\left(5 a^2 b^3 c^4\right)^4\left(6 a^3 b^4 c^2\right) and write the variables in alphabetical order. This involves applying the rules of exponents and simplifying the resulting expression.

Understanding Exponents

Exponents are a shorthand way of representing repeated multiplication. For example, a3a^3 means a×a×aa \times a \times a. When we have an expression raised to a power, such as (5a2b3c4)4\left(5 a^2 b^3 c^4\right)^4, we need to apply the exponent to each part of the expression.

Simplifying the Expression

To simplify the given expression, we will first apply the exponent to each part of the expression. This involves multiplying the exponent by each of the exponents in the expression.

Step 1: Apply the Exponent to Each Part of the Expression

We will start by applying the exponent to the first part of the expression, (5a2b3c4)4\left(5 a^2 b^3 c^4\right)^4. This involves multiplying the exponent by each of the exponents in the expression.

(5a2b3c4)4=54×a2×4×b3×4×c4×4\left(5 a^2 b^3 c^4\right)^4 = 5^4 \times a^{2 \times 4} \times b^{3 \times 4} \times c^{4 \times 4}

Step 2: Simplify the Expression

Now that we have applied the exponent to each part of the expression, we can simplify the resulting expression.

54×a2×4×b3×4×c4×4=625×a8×b12×c165^4 \times a^{2 \times 4} \times b^{3 \times 4} \times c^{4 \times 4} = 625 \times a^8 \times b^{12} \times c^{16}

Step 3: Multiply the Two Expressions

Now that we have simplified the first part of the expression, we can multiply it by the second part of the expression, (6a3b4c2)\left(6 a^3 b^4 c^2\right).

625×a8×b12×c16×6×a3×b4×c2625 \times a^8 \times b^{12} \times c^{16} \times 6 \times a^3 \times b^4 \times c^2

Step 4: Simplify the Resulting Expression

Now that we have multiplied the two expressions, we can simplify the resulting expression.

625×a8×b12×c16×6×a3×b4×c2=3750×a11×b16×c18625 \times a^8 \times b^{12} \times c^{16} \times 6 \times a^3 \times b^4 \times c^2 = 3750 \times a^{11} \times b^{16} \times c^{18}

Writing the Variables in Alphabetical Order

Now that we have simplified the expression, we can write the variables in alphabetical order.

3750×a11×b16×c183750 \times a^{11} \times b^{16} \times c^{18}

Conclusion

In this article, we simplified the given expression (5a2b3c4)4(6a3b4c2)\left(5 a^2 b^3 c^4\right)^4\left(6 a^3 b^4 c^2\right) and wrote the variables in alphabetical order. This involved applying the rules of exponents and simplifying the resulting expression.

Frequently Asked Questions

Q: What is the simplified expression?

A: The simplified expression is 3750×a11×b16×c183750 \times a^{11} \times b^{16} \times c^{18}.

Q: How do I apply the exponent to each part of the expression?

A: To apply the exponent to each part of the expression, you need to multiply the exponent by each of the exponents in the expression.

Q: How do I simplify the resulting expression?

A: To simplify the resulting expression, you need to multiply the two expressions together and then simplify the resulting expression.

Final Answer

The final answer is 3750×a11×b16×c18\boxed{3750 \times a^{11} \times b^{16} \times c^{18}}.

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Introduction

In our previous article, we simplified the given expression (5a2b3c4)4(6a3b4c2)\left(5 a^2 b^3 c^4\right)^4\left(6 a^3 b^4 c^2\right) and wrote the variables in alphabetical order. In this article, we will provide a Q&A guide to help you understand the process of simplifying the expression and writing the variables in alphabetical order.

Q&A Guide

Q: What is the first step in simplifying the expression?

A: The first step in simplifying the expression is to apply the exponent to each part of the expression. This involves multiplying the exponent by each of the exponents in the expression.

Q: How do I apply the exponent to each part of the expression?

A: To apply the exponent to each part of the expression, you need to multiply the exponent by each of the exponents in the expression. For example, if you have the expression (5a2b3c4)4\left(5 a^2 b^3 c^4\right)^4, you would multiply the exponent by each of the exponents in the expression: 54×a2×4×b3×4×c4×45^4 \times a^{2 \times 4} \times b^{3 \times 4} \times c^{4 \times 4}.

Q: What is the next step in simplifying the expression?

A: The next step in simplifying the expression is to simplify the resulting expression. This involves multiplying the two expressions together and then simplifying the resulting expression.

Q: How do I simplify the resulting expression?

A: To simplify the resulting expression, you need to multiply the two expressions together and then simplify the resulting expression. For example, if you have the expression 625×a8×b12×c16×6×a3×b4×c2625 \times a^8 \times b^{12} \times c^{16} \times 6 \times a^3 \times b^4 \times c^2, you would multiply the two expressions together and then simplify the resulting expression: 3750×a11×b16×c183750 \times a^{11} \times b^{16} \times c^{18}.

Q: How do I write the variables in alphabetical order?

A: To write the variables in alphabetical order, you need to arrange the variables in the expression in alphabetical order. For example, if you have the expression 3750×a11×b16×c183750 \times a^{11} \times b^{16} \times c^{18}, you would arrange the variables in alphabetical order: 3750×a11×b16×c183750 \times a^{11} \times b^{16} \times c^{18}.

Q: What is the final answer?

A: The final answer is 3750×a11×b16×c18\boxed{3750 \times a^{11} \times b^{16} \times c^{18}}.

Common Mistakes

Mistake 1: Not Applying the Exponent to Each Part of the Expression

A common mistake when simplifying the expression is not applying the exponent to each part of the expression. This can result in an incorrect simplified expression.

Mistake 2: Not Simplifying the Resulting Expression

Another common mistake when simplifying the expression is not simplifying the resulting expression. This can result in an incorrect simplified expression.

Mistake 3: Not Writing the Variables in Alphabetical Order

A common mistake when writing the variables in alphabetical order is not arranging the variables in the expression in alphabetical order. This can result in an incorrect expression.

Conclusion

In this article, we provided a Q&A guide to help you understand the process of simplifying the expression and writing the variables in alphabetical order. We also discussed common mistakes to avoid when simplifying the expression.

Frequently Asked Questions

Q: What is the first step in simplifying the expression?

A: The first step in simplifying the expression is to apply the exponent to each part of the expression.

Q: How do I apply the exponent to each part of the expression?

A: To apply the exponent to each part of the expression, you need to multiply the exponent by each of the exponents in the expression.

Q: What is the next step in simplifying the expression?

A: The next step in simplifying the expression is to simplify the resulting expression.

Q: How do I simplify the resulting expression?

A: To simplify the resulting expression, you need to multiply the two expressions together and then simplify the resulting expression.

Final Answer

The final answer is 3750×a11×b16×c18\boxed{3750 \times a^{11} \times b^{16} \times c^{18}}.