(1331)– (2/3)

For a positive base a and a rational exponent of the form p/q, the rule ap/q means: take the q-th root of a, then raise that result to the power p. A negative exponent a-n means the reciprocal of an, that is 1/an. Combining both rules, a negative fractional exponent a-p/q equals 1 divided by (the q-th root of a) raised to the power p.

1. Express 1331 as a perfect cube: 1331 = 113 (since 11 × 11 × 11 = 1331).

2. Rewrite the original expression using this cube: (113)-2/3.

3. Apply the power-of-a-power rule (multiply the exponents): 3 × (-2/3) = -2, so the expression becomes 11-2.

4. Apply the negative exponent rule: 11-2 = 1/(112) = 1/121.

Cross-check: the cube root of 1331 is 11 (since 11 × 11 × 11 = 1331); squaring 11 gives 121; taking the reciprocal (because the exponent is negative) gives 1/121 — this matches the step-by-step result above.