The image contains a math problem involving exponents and radical expressions. I will analyze the image to extract the mathematical content and provide a solution.

Extracted Problem

The problem appears to involve rewriting an expression with a negative exponent. The expression given in the image is:

$\left( \frac{x^4}{y^5} \right)^{-3}$

Solution

To simplify the expression with a negative exponent, we can use the rule:

$a^{-n} = \frac{1}{a^n}$

Applying this rule to the entire expression:

$\left( \frac{x^4}{y^5} \right)^{-3} = \frac{1}{\left( \frac{x^4}{y^5} \right)^3}$

Now, apply the exponent to both the numerator and the denominator:

$\frac{1}{\frac{x^{4 \cdot 3}}{y^{5 \cdot 3}}} = \frac{1}{\frac{x^{12}}{y^{15}}}$

To simplify further, take the reciprocal:

$\frac{y^{15}}{x^{12}}$

Final Answer

$\boxed{\frac{y^{15}}{x^{12}}}$

Would you like more details, or do you have any questions?

Related Questions

1. What are the rules for simplifying expressions with exponents?
2. How do you simplify expressions with fractional exponents?
3. How does the power of a quotient rule work with different bases?
4. What is the importance of understanding negative exponents?
5. How do you convert expressions with exponents to radical form?

Tip

Remember, when dealing with negative exponents, the base and its exponent simply switch to their reciprocal position and the exponent becomes positive.