Revision: a) 9² x 9⁻², b) 4⁵ / 4⁻², c) 5³ + 3⁵, d) 5⁰ - 1⁴, e) (14.2)⁴ x (14.2)¹/4, f) (14.2)⁴ + (14.2)¹/4

We use the exponent rule $a^m \times a^n = a^{m+n}$.

$$9^2 \times 9^{-2} = 9^{2 + (-2)}$$ $$= 9^{2-2}$$ $$= 9^0$$

We use the exponent rule $a^0 = 1$.

$$= 1$$

The answer for a) is $\boxed{\text{1}}$.

We use the exponent rule $a^m \div a^n = a^{m-n}$.

$$4^5 \div 4^{-2} = 4^{5 - (-2)}$$ $$= 4^{5+2}$$ $$= 4^7$$

Now we calculate the value of $4^7$.

$$4^7 = 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4$$ $$= 16384$$

The answer for b) is $\boxed{\text{16384}}$.

We calculate each term separately and then add them.

$$5^3 = 5 \times 5 \times 5 = 125$$ $$3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243$$

Now we add the results.

$$5^3 + 3^5 = 125 + 243$$ $$= 368$$

The answer for c) is $\boxed{\text{368}}$.

We use the exponent rule $a^0 = 1$.

$$5^0 = 1$$

We calculate $1^4$.

$$1^4 = 1 \times 1 \times 1 \times 1 = 1$$

Now we subtract the results.

$$5^0 - 1^4 = 1 - 1$$ $$= 0$$

The answer for d) is $\boxed{\text{0}}$.

We use the exponent rule $a^m \times a^n = a^{m+n}$.

$$(14.2)^4 \times (14.2)^{\frac{1}{4}} = (14.2)^{4 + \frac{1}{4}}$$

To add the exponents, we find a common denominator.

$$4 + \frac{1}{4} = \frac{16}{4} + \frac{1}{4} = \frac{17}{4}$$

So the expression simplifies to:

$$= (14.2)^{\frac{17}{4}}$$

The answer for e) is $\boxed{(14.2)^{\frac{17}{4}}}$.

We calculate each term separately and then add them.

$$(14.2)^4 = 14.2 \times 14.2 \times 14.2 \times 14.2 = 40603.0016$$ $$(14.2)^{\frac{1}{4}} = \sqrt[4]{14.2} \approx 1.940081$$

Now we add the results.

$$(14.2)^4 + (14.2)^{\frac{1}{4}} \approx 40603.0016 + 1.940081$$ $$\approx 40604.941681$$

The answer for f) is approximately $\boxed{\text{40604.941681}}$.