The expression shown in the image is:

$\left( \frac{x^{-6}}{2w^5} \right)^{-3}$

Step-by-step simplification:

1. Apply the exponent to both the numerator and the denominator:

   $\left( \frac{x^{-6}}{2w^5} \right)^{-3} = \frac{\left( x^{-6} \right)^{-3}}{\left( 2w^5 \right)^{-3}}$

2. Simplify each part:

   • For the numerator: $\left( x^{-6} \right)^{-3} = x^{18}$, since $(a^m)^n = a^{m \cdot n}$.
   • For the denominator: $\left( 2w^5 \right)^{-3} = 2^{-3}w^{-15} = \frac{1}{2^3 w^{15}} = \frac{1}{8w^{15}}$.

3. Simplify the entire fraction:

   $\frac{x^{18}}{\frac{1}{8w^{15}}} = x^{18} \cdot \frac{8w^{15}}{1} = 8x^{18}w^{15}$

Final simplified expression:

$8x^{18}w^{15}$

Would you like any further details or have any questions?

Related Questions:

1. How would the result change if the exponent were $-2$ instead of $-3$?
2. Can you explain the general rule for handling negative exponents in fractions?
3. How would you approach the problem if the denominator contained a variable with a negative exponent?
4. How would this expression change if there were additional variables in the denominator?
5. What happens if the expression inside the parentheses was a polynomial instead of a monomial?

Tip:

Always remember that a negative exponent "flips" the base when simplifying expressions, whether it's part of a fraction or a single term.