Let's simplify the expression step by step:

The given expression is:

\[
\frac{24x^6y^4}{3x^2y^2} \div 4x^3
\]

### Step 1: Simplify the first division
\[
\frac{24x^6y^4}{3x^2y^2}
\]
Divide the coefficients:
\[
\frac{24}{3} = 8
\]

Now, subtract the exponents of \(x\) and \(y\) (using the rule \(\frac{a^m}{a^n} = a^{m-n}\)):

For \(x\):
\[
x^{6-2} = x^4
\]

For \(y\):
\[
y^{4-2} = y^2
\]

Thus, the expression simplifies to:
\[
8x^4y^2
\]

### Step 2: Divide by \(4x^3\)
Now, simplify:
\[
\frac{8x^4y^2}{4x^3}
\]

Divide the coefficients:
\[
\frac{8}{4} = 2
\]

Now, subtract the exponents of \(x\):
\[
x^{4-3} = x^1 = x
\]

So, the final expression is:
\[
2xy^2
\]

### Final Answer:
\[
2xy^2
\]

Would you like further details or have any questions?

Here are five related questions:
1. How would you simplify the expression \(\frac{15x^5y^3}{5x^2y}\)?
2. What is the result of dividing \(48x^7y^5\) by \(6x^4y^3\)?
3. How do you apply exponent rules when dividing monomials?
4. Can you simplify the expression \(18x^9y^6 \div 6x^5y^3\)?
5. What happens when you divide a variable raised to the same power, like \(\frac{x^n}{x^n}\)?

**Tip:** When dividing terms with exponents, always remember to subtract the exponents of like variables.

Learn how to simplify the algebraic expression 24x⁶y⁴ ÷ 3x²y² ÷ 4x³ step-by-step. This tutorial covers key algebraic concepts, including exponent rules and dividing monomials. Ideal for students in Grades 8-10.

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