Find the prime factorizations in exponential notation for 900, 810, 4725, and 7500.

$$900 = 2 \times 450$$ $$450 = 2 \times 225$$ $$225 = 3 \times 75$$ $$75 = 3 \times 25$$ $$25 = 5 \times 5$$

$$900 = 2 \times 2 \times 3 \times 3 \times 5 \times 5 = 2^2 \times 3^2 \times 5^2$$

The exponential notation is $\boxed{2^2 \times 3^2 \times 5^2}$.

$$810 = 2 \times 405$$ $$405 = 3 \times 135$$ $$135 = 3 \times 45$$ $$45 = 3 \times 15$$ $$15 = 3 \times 5$$

$$810 = 2 \times 3 \times 3 \times 3 \times 3 \times 5 = 2^1 \times 3^4 \times 5^1$$

The exponential notation is $\boxed{2 \times 3^4 \times 5}$.

$$4725 = 3 \times 1575$$ $$1575 = 3 \times 525$$ $$525 = 3 \times 175$$ $$175 = 5 \times 35$$ $$35 = 5 \times 7$$

$$4725 = 3 \times 3 \times 3 \times 5 \times 5 \times 7 = 3^3 \times 5^2 \times 7^1$$

The exponential notation is $\boxed{3^3 \times 5^2 \times 7}$.

$$7500 = 2 \times 3750$$ $$3750 = 2 \times 1875$$ $$1875 = 3 \times 625$$ $$625 = 5 \times 125$$ $$125 = 5 \times 25$$ $$25 = 5 \times 5$$

$$7500 = 2 \times 2 \times 3 \times 5 \times 5 \times 5 \times 5 = 2^2 \times 3^1 \times 5^4$$

The exponential notation is $\boxed{2^2 \times 3 \times 5^4}$.