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The problem asks you to simplify the expression:

\[
\frac{-4x^4}{\frac{3}{4}x^5}
\]

Let's go step by step:

1. **Simplify the constants**: The expression has a \(-4\) in the numerator and \(\frac{3}{4}\) in the denominator. To simplify:
   
   \[
   \frac{-4}{\frac{3}{4}} = -4 \times \frac{4}{3} = \frac{-16}{3}
   \]

2. **Simplify the variables**: The expression has \(x^4\) in the numerator and \(x^5\) in the denominator. When you divide \(x^4\) by \(x^5\), subtract the exponents:

   \[
   x^{4-5} = x^{-1} = \frac{1}{x}
   \]

So the simplified expression is:

\[
\frac{-16}{3} \times \frac{1}{x} = \frac{-16}{3x}
\]

Thus, the simplified expression is:

\[
\boxed{\frac{-16}{3x}}
\]

Would you like more details, or do you have any questions?

Here are 5 related questions you might find interesting:
1. How do you simplify expressions with negative exponents?
2. What are the rules for multiplying and dividing fractions?
3. How would the expression change if the powers of \(x\) were different?
4. What is the general rule for combining like terms in fractions?
5. How do you simplify an expression involving a complex fraction?

**Tip:** Always remember to simplify the coefficients and the variable parts separately when working with algebraic fractions.

Simplify the rational expression -4x^4 / (3/4)x^5 using algebraic rules, including simplifying fractions and exponents. Learn the step-by-step process to reach the simplified form. Suitable for students in Grades 8-10.

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