using four unit multiplierss to convert cubic meters to milliliters

Question

I am given the following problem in Algebra:

 

Use four unit multipliers to convert 400 cubic meters to milliliters. (Do not multiply out).

 

I solved it in the manner which follows:

 

400 m × 100 cm/1 m × 100 cm/1 m × 100 cm/1 m × 10 mm/1 cm × 10 mm/1 cm × 10 mm/1 cm

 

Is this correct? Thank you.

Answer 1

Wow, James, six is not four.

 

400 m³ x 100 cm/1 m x 10,000 cm²/1 m² x 10 mm/1 cm x 100 mm²/1 cm²