Find the value of (0.04)-1.5

Solution:

1. Rewrite the exponent: -1.5 = -3/2, so (0.04)^{-1.5} = (0.04)^{-3/2} = 1/(0.04^{3/2}).

2. Compute 0.04^{3/2} as (sqrt(0.04))^3. Since sqrt(0.04)=0.2, we get 0.2^3 = 0.008.

3. Take the reciprocal: 1/0.008 = 125. Therefore (0.04)^{-1.5} = 125.

Alternative quick method:

• Note that 0.04 = 1/25 = 25^{-1}. Then (0.04)^{-1.5} = (25^{-1})^{-3/2} = 25^{3/2}.

• Compute 25^{3/2} = (sqrt(25))^3 = 5^3 = 125.

Answer: 125