To simplify the expression $\dfrac{5^{10}}{5^{12}}$, we can use the rule of exponents:

$\dfrac{a^m}{a^n} = a^{m-n}$

where $a$ is a non-zero base, and $m$ and $n$ are exponents. Applying this rule to the given expression:

$\dfrac{5^{10}}{5^{12}} = 5^{10-12}$

Simplifying the exponent:

$5^{10-12} = 5^{-2}$

Since $5^{-2}$ represents the reciprocal of $5^2$, we can express it as:

$5^{-2} = \dfrac{1}{5^2}$

Calculating $5^2$:

$5^2 = 25$

So:

$\dfrac{1}{5^2} = \dfrac{1}{25}$

Thus, the simplified value of $\dfrac{5^{10}}{5^{12}}$ is:

$\dfrac{5^{10}}{5^{12}} = \dfrac{1}{25}$

Would you like more details or have any questions?

Related Questions:

1. What is the result of $\dfrac{7^5}{7^8}$?
2. How would you simplify $\dfrac{3^{15}}{3^{10}}$?
3. Can you explain the properties of exponents in general?
4. How do negative exponents work and why are they considered as reciprocals?
5. What happens when the base is a fraction or a decimal instead of an integer?

Tip: When dividing powers with the same base, simply subtract the exponents.