(-1 over 5 k power of 5 m power of 3)power of 3

We are asked to simplify the expression:

\[
\left(\frac{-1}{5}k^5 m^3\right)^3
\]

### Step-by-Step Simplification:

1. **Apply the power to each part of the expression:**
   \[
   \left(\frac{-1}{5}k^5 m^3\right)^3 = \frac{(-1)^3}{5^3} (k^5)^3 (m^3)^3
   \]

2. **Simplify each part:**
   - \((-1)^3 = -1\)
   - \(5^3 = 125\)
   - \((k^5)^3 = k^{15}\) (multiply the exponents)
   - \((m^3)^3 = m^9\)

3. **Put it all together:**
   \[
   \frac{-1}{125} k^{15} m^9
   \]

Thus, the simplified expression is:

\[
\frac{-1}{125} k^{15} m^9
\]

Would you like further explanation or have any questions about this solution?

Here are 5 related questions:
1. How do you simplify an expression with multiple variables raised to powers?
2. What is the rule for multiplying exponents when raising a power to a power?
3. Can you explain how to handle negative bases in exponentiation?
4. How do you apply exponent rules to fractions?
5. How do you simplify expressions involving negative exponents?

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

(-1 over 5 k power of 5 m power of 3) power of 3

Learn how to simplify the expression (-1/5 k^5 m^3)^3 using exponent rules. This step-by-step guide covers key algebraic concepts, including exponentiation of fractions and variables, and is suitable for students in Grades 8-10.

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