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.

Learn how to simplify the division of powers problem \( \frac{5^{10}}{5^{12}} \). Understand the rule of exponents and how to apply it correctly. Suitable for Grades 7-9 students studying algebra and exponents.

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