1km2 = 1 * 10^10 cm2 -- HUH?

Question

1km2 = 1 * 10^6 m2

How come 1km2 = 1 * 10^10 cm2 ?

It doesn't make sense to me as I thought the metric unit changes were like this
1km = 1*10^3m = 1*10^6cm
1km2 = 1*10^(3+3)m2 = 1*10^(6+3)
and so on..

Answer 1

1 km² = 1000 x 1000 m²
1 km² = 10³ x 10³ m²
1 km² = 10^6 m²

1m² = 100 x 100 cm²
1 m² = 10^4 cm²

1 km² = 10^6 m² = 10^6 x 10^4 cm² = 10^10 cm²

Answer 2

1 km = 1000m
1m = 100 cm
1km = 100,000 cm = 10^5 cm

1 km^2 = (10^5)^2 = 10^10 cm^2

Answer 3

1km = 10^5 cm
=> 1km^2 = 10^10 cm^2
You got it right!