`1 g cm^(-3) = 1000 kg m^(-3)`

Answer

To prove that \(1 \, \text{g cm}^{-3} = 1000 \, \text{kg m}^{-3}\), we will convert the units on the left side to the units on the right side.

### Step-by-Step Solution:

1. **Understand the Units**:
- We need to convert grams to kilograms and cubic centimeters to cubic meters.

2. **Convert Kilograms to Grams**:
- We know that \(1 \, \text{kg} = 1000 \, \text{g}\).
- Therefore, \(1000 \, \text{kg} = 1000 \times 1000 \, \text{g} = 10^6 \, \text{g}\).

3. **Convert Meters to Centimeters**:
- We know that \(1 \, \text{m} = 100 \, \text{cm}\).
- Therefore, \(1 \, \text{m}^3 = (100 \, \text{cm})^3 = 100^3 \, \text{cm}^3 = 10^6 \, \text{cm}^3\).

4. **Set Up the Conversion**:
- Now we can express \(1000 \, \text{kg m}^{-3}\) in terms of grams and cubic centimeters:
\[ 1000 \, \text{kg m}^{-3} = \frac{10^6 \, \text{g}}{10^6 \, \text{cm}^3} \]

5. **Simplify the Expression**:
- This simplifies to:
\[ \frac{10^6 \, \text{g}}{10^6 \, \text{cm}^3} = 1 \, \text{g cm}^{-3} \]

6. **Conclusion**:
- Therefore, we have shown that:
\[ 1 \, \text{g cm}^{-3} = 1000 \, \text{kg m}^{-3} \]
- The statement is correct.