1 kg m² s⁻² = ...... g cm² s⁻²

The correct answer is 10⁷ g cm² s⁻².

To convert the unit from the SI system (kg m² s⁻²) to the CGS system (g cm² s⁻²), we can perform a step-by-step conversion of each individual base unit:
1. Convert kilograms (kg) to grams (g):
1 kg = 10³ g
2. Convert meters (m) to centimeters (cm):
1 m = 10² cm
Therefore, squaring both sides gives:
1 m² = (10² cm)² = 10⁴ cm²
3. The unit of time, seconds (s), remains the same in both systems:
1 s⁻² = 1 s⁻²

Now, we substitute these conversion factors into the original expression:
1 kg m² s⁻² = (1 kg) × (1 m²) × (1 s⁻²)
1 kg m² s⁻² = (10³ g) × (10⁴ cm²) × (1 s⁻²)
Using the laws of exponents, we multiply the powers of 10:
10³ × 10⁴ = 10^(3 + 4) = 10⁷

Thus, we find:
1 kg m² s⁻² = 10⁷ g cm² s⁻²