Let's solve the problem step by step, focusing on simplifying the expressions.

We are given two expressions to multiply, and the goal is to rewrite them with the simplest base and only positive exponents.

Expression 1 (left):

$\left( \frac{-60}{z^{60}} \cdot \frac{20}{6470} \cdot \frac{-7}{x^{50}} \cdot \frac{85}{s^{23}} \cdot \frac{8}{4} \right) \times \frac{z^{25} 8^{8} x^{6} s^{-28}}{1}$

Expression 2 (right):

$\left( \frac{-140}{z^{40}} \cdot \frac{24}{770} \cdot \frac{-55}{x^{50}} \cdot \frac{40}{s^{20}} \cdot \frac{-3}{4} \right) \times \frac{z^{55} 7^{8} x^{6} s^{-18}}{1}$

Steps for Simplification:

1. Simplify the constants:

   • Multiply the numerical constants.

2. Combine powers of each variable (z, x, s, etc.):

   • Use the laws of exponents: $a^m \cdot a^n = a^{m+n}$.

3. Ensure all exponents are positive:

   • If any variable has a negative exponent, shift it to the denominator or numerator as needed.

Let me now compute the simplification step by step.The simplified expression is:

$\frac{-1.54 \times 10^{20}}{z^{20} x^{88} s^{89}}$

This is the most simplified form, with only positive exponents and all terms in the denominator.

Would you like further details on any of the steps?

Related Questions:

1. How do you apply the laws of exponents when multiplying variables?
2. What are the common mistakes when simplifying complex algebraic fractions?
3. Why do negative exponents move terms from the numerator to the denominator?
4. How can you simplify an expression with multiple variables efficiently?
5. What role does combining like terms play in simplifying expressions?

Tip:

When simplifying expressions with multiple variables, always combine the exponents of like bases first before handling numerical coefficients.