`root3(-m^6)=………..`

Answer

To solve the expression \( \sqrt[3]{-m^6} \), we can follow these steps:

### Step-by-Step Solution:

1. **Rewrite the expression**: Start with the expression \( \sqrt[3]{-m^6} \).
\[ \sqrt[3]{-m^6} = (-m^6)^{\frac{1}{3}} \]

2. **Apply the power of a product rule**: We can separate the negative sign and the variable:
\[ (-m^6)^{\frac{1}{3}} = (-1)^{\frac{1}{3}} \cdot (m^6)^{\frac{1}{3}} \]

3. **Evaluate the cube root of -1**: The cube root of -1 is -1.
\[ (-1)^{\frac{1}{3}} = -1 \]

4. **Evaluate the cube root of \( m^6 \)**: Using the power rule \( (a^m)^n = a^{m \cdot n} \):
\[ (m^6)^{\frac{1}{3}} = m^{6 \cdot \frac{1}{3}} = m^2 \]

5. **Combine the results**: Now combine the results from steps 3 and 4:
\[ \sqrt[3]{-m^6} = -1 \cdot m^2 = -m^2 \]

### Final Answer:
\[ \sqrt[3]{-m^6} = -m^2 \]