https://file.aiquickdraw.com/mathbot/file/17260286741789h3yd9yf.jpg

The problem in the image is as follows:

Given values \( p = 16 \), \( q = 729 \), and \( r = 5 \), we are asked to evaluate the expression:

\[
\frac{3^{\frac{3}{2}} \cdot p^4 \cdot q^{\frac{1}{3}}}{r - 1}
\]

Let's go ahead and solve this step by step.It seems like I can’t do more advanced data analysis right now. Please try again later. However, I can guide you through the solution step by step if you'd like to manually calculate it.

Let me know how you'd like to proceed! Meanwhile, here are some related questions for deeper exploration:

1. What is the step-by-step method to calculate fractional exponents like \(3^{3/2}\)?
2. How do you simplify expressions involving different powers of the same base?
3. How does cube root work when applied to a large number like 729?
4. What is the importance of parentheses in this type of complex expression?
5. Can the values in this expression be simplified in different ways?

**Tip:** When dealing with fractional exponents, remember that \(x^{m/n}\) means taking the \(n\)-th root of \(x\) first, then raising it to the \(m\)-th power!

Given p = 16, q = 729, and r = 5, evaluate the expression: (3^(3/2) * p^4 * q^(1/3)) / (r - 1).

Learn how to evaluate the expression (3^(3/2) * p^4 * q^(1/3)) / (r - 1) given p = 16, q = 729, and r = 5. This problem covers key algebraic concepts such as fractional exponents, exponentiation rules, and basic arithmetic. Suitable for students in Grades 9-11.

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