Simplify The Expression: 3 2 × 4 5 × 18 4 × 36 \frac{3^2 \times 4^5 \times 18}{4 \times 36} 4 × 36 3 2 × 4 5 × 18

Mar 12, 2025 by ADMIN 116 views

Simplify the Expression: A Step-by-Step Guide to Evaluating the Given Mathematical Expression

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Introduction

In mathematics, simplifying expressions is a crucial skill that helps us evaluate complex mathematical problems efficiently. The given expression, $\frac{3^2 \times 4^5 \times 18}{4 \times 36}$ , requires us to simplify it using various mathematical operations and properties. In this article, we will break down the expression into manageable parts, apply the necessary mathematical rules, and simplify it step by step.

Breaking Down the Expression

The given expression is a fraction, and we can start by breaking it down into its numerator and denominator. The numerator is $3^2 \times 4^5 \times 18$ , and the denominator is $4 \times 36$ . To simplify the expression, we need to apply various mathematical operations and properties.

Simplifying the Numerator

The numerator is $3^2 \times 4^5 \times 18$ . We can start by simplifying the exponentiation. $3^2$ is equal to $9$ , and $4^5$ is equal to $1024$ . Therefore, the numerator becomes $9 \times 1024 \times 18$ .

Simplifying the Denominator

The denominator is $4 \times 36$ . We can simplify this by multiplying $4$ and $36$ . $4 \times 36$ is equal to $144$ .

Applying Mathematical Properties

Now that we have simplified the numerator and denominator, we can apply various mathematical properties to simplify the expression further. One of the properties we can use is the commutative property of multiplication, which states that the order of the factors does not change the product.

Canceling Common Factors

We can see that both the numerator and denominator have a common factor of $4$ . We can cancel this common factor by dividing both the numerator and denominator by $4$ . This simplifies the expression to $\frac{9 \times 256 \times 18}{36}$ .

Simplifying the Expression Further

We can simplify the expression further by canceling common factors. Both the numerator and denominator have a common factor of $9$ . We can cancel this common factor by dividing both the numerator and denominator by $9$ . This simplifies the expression to $\frac{256 \times 18}{4}$ .

Evaluating the Expression

Now that we have simplified the expression, we can evaluate it by multiplying the numerator and denominator. The numerator is $256 \times 18$ , and the denominator is $4$ . Multiplying the numerator and denominator gives us $\frac{4608}{4}$ .

Final Answer

The final answer is $\frac{4608}{4}$ , which simplifies to $1152$ .

Conclusion

In this article, we simplified the given expression, $\frac{3^2 \times 4^5 \times 18}{4 \times 36}$ , using various mathematical operations and properties. We broke down the expression into manageable parts, applied the necessary mathematical rules, and simplified it step by step. The final answer is $1152$ .

Frequently Asked Questions

Q: What is the given expression?

A: The given expression is $\frac{3^2 \times 4^5 \times 18}{4 \times 36}$ .

Q: How do we simplify the expression?

A: We simplify the expression by breaking it down into manageable parts, applying various mathematical operations and properties, and canceling common factors.

Q: What is the final answer?

A: The final answer is $1152$ .

Q: What mathematical properties do we use to simplify the expression?

A: We use the commutative property of multiplication, the associative property of multiplication, and the distributive property of multiplication over addition to simplify the expression.

Q: How do we evaluate the expression?

A: We evaluate the expression by multiplying the numerator and denominator.

Step-by-Step Solution

Step 1: Break down the expression into its numerator and denominator.

The numerator is $3^2 \times 4^5 \times 18$ , and the denominator is $4 \times 36$ .

Step 2: Simplify the exponentiation in the numerator.

$3^2$ is equal to $9$ , and $4^5$ is equal to $1024$ . Therefore, the numerator becomes $9 \times 1024 \times 18$ .

Step 3: Simplify the denominator.

$4 \times 36$ is equal to $144$ .

Step 4: Apply the commutative property of multiplication.

Step 5: Cancel common factors.

Both the numerator and denominator have a common factor of $9$ . We can cancel this common factor by dividing both the numerator and denominator by $9$ . This simplifies the expression to $\frac{256 \times 18}{4}$ .

Step 6: Evaluate the expression.

The numerator is $256 \times 18$ , and the denominator is $4$ . Multiplying the numerator and denominator gives us $\frac{4608}{4}$ .

Step 7: Simplify the expression further.

$\frac{4608}{4}$ simplifies to $1152$ .

Final Answer

The final answer is $\boxed{1152}$ .

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Introduction

In our previous article, we simplified the given expression, $\frac{3^2 \times 4^5 \times 18}{4 \times 36}$ , using various mathematical operations and properties. In this article, we will provide a Q&A guide to help you understand the steps involved in simplifying the expression.

Frequently Asked Questions

Q: What is the given expression?

A: The given expression is $\frac{3^2 \times 4^5 \times 18}{4 \times 36}$ .

Q: How do we simplify the expression?

A: We simplify the expression by breaking it down into manageable parts, applying various mathematical operations and properties, and canceling common factors.

Q: What is the final answer?

A: The final answer is $1152$ .

Q: What mathematical properties do we use to simplify the expression?

A: We use the commutative property of multiplication, the associative property of multiplication, and the distributive property of multiplication over addition to simplify the expression.

Q: How do we evaluate the expression?

A: We evaluate the expression by multiplying the numerator and denominator.

Step-by-Step Solution

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

A: The first step is to break down the expression into its numerator and denominator.

Q: What is the numerator of the expression?

A: The numerator is $3^2 \times 4^5 \times 18$ .

Q: What is the denominator of the expression?

A: The denominator is $4 \times 36$ .

Q: How do we simplify the exponentiation in the numerator?

A: We simplify the exponentiation by evaluating $3^2$ and $4^5$ . $3^2$ is equal to $9$ , and $4^5$ is equal to $1024$ . Therefore, the numerator becomes $9 \times 1024 \times 18$ .

Q: How do we simplify the denominator?

A: We simplify the denominator by multiplying $4$ and $36$ . $4 \times 36$ is equal to $144$ .

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

A: The next step is to apply the commutative property of multiplication.

Q: How do we apply the commutative property of multiplication?

A: We can see that both the numerator and denominator have a common factor of $4$ . We can cancel this common factor by dividing both the numerator and denominator by $4$ . This simplifies the expression to $\frac{9 \times 256 \times 18}{36}$ .

Q: How do we simplify the expression further?

A: We can simplify the expression further by canceling common factors. Both the numerator and denominator have a common factor of $9$ . We can cancel this common factor by dividing both the numerator and denominator by $9$ . This simplifies the expression to $\frac{256 \times 18}{4}$ .

Q: How do we evaluate the expression?

A: We evaluate the expression by multiplying the numerator and denominator. The numerator is $256 \times 18$ , and the denominator is $4$ . Multiplying the numerator and denominator gives us $\frac{4608}{4}$ .

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

A: The final step is to simplify the expression further by dividing the numerator and denominator by their greatest common factor.

Q: What is the final answer?

A: The final answer is $1152$ .

Common Mistakes to Avoid

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

A: Some common mistakes to avoid include:

Not breaking down the expression into its numerator and denominator
Not simplifying the exponentiation in the numerator
Not applying the commutative property of multiplication
Not canceling common factors
Not evaluating the expression correctly

Conclusion

In this article, we provided a Q&A guide to help you understand the steps involved in simplifying the expression, $\frac{3^2 \times 4^5 \times 18}{4 \times 36}$ . We covered the first step in simplifying the expression, the next step, and the final step. We also discussed common mistakes to avoid when simplifying the expression.

Final Answer

The final answer is $\boxed{1152}$ .