The given exercise asks to simplify the provided expressions while using only positive exponents and ensuring the simplest base and exponent form.

Problem Overview:

The exercise shows two large fractions being multiplied, each with powers of different variables. The goal is to simplify them entirely.

To proceed, I will break down the process:

1. Simplification of exponents in the numerators and denominators:

- First, analyze the powers of the variables in both the numerator and the denominator.
- Apply the laws of exponents:
    - $$a^m \times a^n = a^{m+n}$$
    - $$\frac{a^m}{a^n} = a^{m-n}$$
    - If the result has negative exponents, they should be converted to positive ones by moving them between numerator and denominator.

2. Apply multiplication and division rules:

- Multiply the numerators of both fractions and the denominators of both fractions together.
- Simplify the resulting terms by combining like bases and using the rules of exponents.

3. Convert any negative exponents:

- Any negative exponents left should be rewritten with positive exponents by moving them to the other side of the fraction.

Let me perform the calculations and provide the simplified form. I’ll begin solving now.The fully simplified expression is:

$\frac{64981512288000000 \cdot x^{131}}{s^{38} \cdot z^{302}}$

This is the simplest form, where all the variables have only positive exponents.

Let me know if you'd like further details or have any questions.

Related Questions:

1. How do you apply the laws of exponents in general?
2. How can you simplify expressions with negative exponents?
3. What are some tips for multiplying fractions with exponents?
4. Can you explain the rule for converting negative exponents to positive ones?
5. How would you handle complex fractions that include both multiplication and division of exponents?

Tip:

Always remember to keep track of both the numerator and denominator carefully, especially when simplifying large expressions with multiple variables.