Find the value of (0.04)-1.5.

Concept: For a nonzero base a, a negative exponent inverts the base: a-n = 1/an.

A fractional exponent combines a root with a power: ap/q equals the q-th root of a, raised to the power p — so a3/2 = (square root of a)3.

These rules apply directly once a decimal base is rewritten as a simple fraction.

1. Rewrite 0.04 as a fraction: 0.04 = 4/100 = 1/25.

2. Apply the negative-exponent rule: (1/25)-1.5 = 251.5 — inverting the base flips the sign of the exponent.

3. Rewrite 25 as 52: 251.5 = (52)1.5 = 53 — using (am)n = amn.

4. Compute 53 = 125.

Cross-check: computing the original expression directly gives 0.041.5 = 0.04 x 0.040.5 = 0.04 x 0.2 = 0.008, so 0.04-1.5 = 1/0.008 = 125 — matching the result above.