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.