https://file.aiquickdraw.com/mathbot/file/1726439296960gpwmh82c.jpg

The given expression from the image is:

\[
\frac{(8x^5y^3)}{(4x^2y^1)}
\]

Let’s simplify this step-by-step:

1. **Coefficients**: Divide \(8\) by \(4\):

\[
\frac{8}{4} = 2
\]

2. **For the variable \(x\)**: Use the rule \(\frac{x^a}{x^b} = x^{a-b}\):

\[
\frac{x^5}{x^2} = x^{5-2} = x^3
\]

3. **For the variable \(y\)**: Similarly, use the rule \(\frac{y^a}{y^b} = y^{a-b}\):

\[
\frac{y^3}{y^1} = y^{3-1} = y^2
\]

Now, combining everything:

\[
\frac{(8x^5y^3)}{(4x^2y^1)} = 2x^3y^2
\]

The simplified expression is:

\[
2x^3y^2
\]

Would you like a more detailed explanation or have any other questions?

Here are 5 related questions:
1. How do you simplify expressions with negative exponents?
2. What is the quotient rule for exponents, and how can it be applied in more complex cases?
3. How can you simplify expressions involving multiple variables with exponents?
4. Can this expression be factored further or manipulated in different ways?
5. What are the key differences between dividing and multiplying powers with exponents?

**Tip**: Always apply the exponent rules carefully, especially when dealing with multiple variables!

Learn how to simplify the algebraic expression (8x^5y^3) ÷ (4x^2y) using exponent rules. This problem demonstrates key algebraic concepts including coefficient division, exponent rules, and variable simplification. Suitable for students in Grades 7-9.

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