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It looks like you uploaded a photo of a math worksheet. The expression you mentioned, \( \left( \frac{-3}{5} a^2 b c^4 \right)^3 \), involves raising a product of terms inside parentheses to a power. 

Let's work through it step by step.

### Simplification of \( \left( \frac{-3}{5} a^2 b c^4 \right)^3 \):

1. **Expand each term within the parentheses**: Each component of the expression inside the parentheses will be raised to the power of 3.

\[
\left( \frac{-3}{5} \right)^3 \times \left( a^2 \right)^3 \times \left( b \right)^3 \times \left( c^4 \right)^3
\]

2. **Calculate each term**:
   - \( \left( \frac{-3}{5} \right)^3 = \frac{(-3)^3}{5^3} = \frac{-27}{125} \)
   - \( \left( a^2 \right)^3 = a^{2 \times 3} = a^6 \)
   - \( \left( b \right)^3 = b^3 \)
   - \( \left( c^4 \right)^3 = c^{4 \times 3} = c^{12} \)

3. **Combine the results**:

\[
\frac{-27}{125} \times a^6 \times b^3 \times c^{12}
\]

### Final Answer:

\[
\frac{-27a^6b^3c^{12}}{125}
\]

Would you like a detailed explanation of any part of the simplification? Here are five related questions you might find interesting:

1. How would the expression change if you raised it to the 4th power instead of the 3rd power?
2. What happens if one of the variables, say \( b \), is set to 0 in the expression?
3. How does the exponentiation affect the sign of the result in this type of expression?
4. How would the simplification differ if the coefficient was positive?
5. Can you expand the expression \( (ab)^n \) where \( n \) is any positive integer?

**Tip:** When raising a fraction to a power, remember to apply the exponent to both the numerator and the denominator separately.

Learn how to simplify the expression ( -3/5 a^2 b c^4 )^3 with a detailed step-by-step solution. This problem involves exponentiation of a product of terms with fractional coefficients and variables. Suitable for high school students studying algebra and exponentiation.

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