- 3 upon 4 x square y × 2 xy cube multiply the following 

Let's multiply the given expression step by step.

The expression is:

\[
\left(-\frac{3}{4}x^2y\right) \times \left(2xy^3\right)
\]

1. **Multiply the coefficients**:
   \[
   -\frac{3}{4} \times 2 = -\frac{3 \times 2}{4} = -\frac{6}{4} = -\frac{3}{2}
   \]

2. **Multiply the \(x\) terms**:
   \[
   x^2 \times x = x^{2+1} = x^3
   \]

3. **Multiply the \(y\) terms**:
   \[
   y \times y^3 = y^{1+3} = y^4
   \]

Now, combine all the terms:

\[
-\frac{3}{2}x^3y^4
\]

So, the product is:

\[
\boxed{-\frac{3}{2}x^3y^4}
\]

Would you like any further details or explanations? Here are some related questions:

1. How do you simplify expressions with fractional coefficients?
2. What is the process for multiplying variables with exponents?
3. How would this expression change if one of the variables had a negative exponent?
4. Can the resulting expression \(-\frac{3}{2}x^3y^4\) be simplified further or factored?
5. How would you divide \(-\frac{3}{2}x^3y^4\) by another monomial?

**Tip:** Always simplify the coefficients first when multiplying algebraic expressions with fractions, and then proceed with the variables.

Learn how to multiply the expression -3/4 x^2 y * 2x y^3 step-by-step with a detailed explanation. This problem covers algebraic multiplication involving fractional coefficients and exponents. Suitable for students in Grades 7-9.

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