1. The problem is to find the reciprocal of an expression involving indices (exponents). 2. The reciprocal of a number or expression $a$ is $\frac{1}{a}$. 3. When dealing with indices, the reciprocal of $a^n$ is $a^{-n}$ because: $$\frac{1}{a^n} = a^{-n}$$ 4. This rule comes from the property of exponents that $a^m \times a^n = a^{m+n}$, so to get the reciprocal, you add the exponent that makes the sum zero. 5. For example, the reciprocal of $x^3$ is $x^{-3}$. 6. Therefore, the reciprocal in indices means changing the sign of the exponent. Final answer: The reciprocal of $a^n$ is $a^{-n}$.