Explanation:

- Let the number be \(x\). Then, the average of the number and its reciprocal is given by \(\frac{x + \frac{1}{x}}{2} = 1\).

- Solve this equation: \(x + \frac{1}{x} = 2\). Multiply through by \(x\) to get: \(x^2 + 1 = 2x\).

- Rearrange to form a quadratic equation: \(x^2 - 2x + 1 = 0\).

- Factorize: \((x-1)^2 = 0\), so \(x = 1\).

- Calculate the average of its square, cube, and fourth power:

- Square: \(1^2 = 1\)

- Cube: \(1^3 = 1\)

- Fourth power: \(1^4 = 1\)

- Average: \(\frac{1 + 1 + 1}{3} = 1\).

- Option 2: 1 is correct.