Express the following in index form: a) 81 b) 1/16. Classify the following as rational or irrational: a) sqrt(2) b) 0.25 c) pi

    $$
    81 = 3 \times 3 \times 3 \times 3
    $$

    $$
    81 = 3^4
    $$
    The index form is $\boxed{3^4}$.

    $$
    16 = 2 \times 2 \times 2 \times 2 = 2^4
    $$

    $$
    \frac{1}{16} = \frac{1}{2^4} = 2^{-4}
    $$
    The index form is $\boxed{2^{-4}}$.

$$
0.25 = \frac{25}{100}
$$

$$
\frac{25}{100} = \frac{1}{4}
$$
Since 0.25 can be expressed as the fraction $\frac{1}{4}$, it is a rational number.  
Therefore, 0.25 is $\boxed{\text{rational}}$.

$\pi$ is the ratio of a circle's circumference to its diameter. Its decimal representation is non-terminating and non-repeating.

Therefore, $\pi$ is $\boxed{\text{irrational}}$.

Therefore, $\frac{7}{4}$ is $\boxed{\text{rational}}$.

The reciprocal of 5 is $\boxed{\frac{1}{5}}$.

The reciprocal of $\frac{2}{3}$ is $\boxed{\frac{3}{2}}$.