Let's simplify the expression:

$\frac{100^{102} - 100^{101}}{100^{101}}$

We can factor out $100^{101}$ from the numerator:

$= \frac{100^{101} \left(100 - 1\right)}{100^{101}}$

Now, cancel the common $100^{101}$ terms from the numerator and the denominator:

$= 100 - 1 = 99$

Thus, the value of the expression is:

$99$

If you'd like further details or have any questions, feel free to ask! Here are some related questions to explore:

1. What happens if we change the base of the exponentiation?
2. How does this simplification technique apply to more complex expressions?
3. What is the result if the exponents were negative?
4. Can this method be used for fractions with different powers in the numerator and denominator?
5. How do exponent rules like $a^m / a^n = a^{m-n}$ work in this context?

Tip: When simplifying expressions involving powers, always look for common terms you can factor out to reduce the complexity of the calculation.