**Simplify.**
*Rewrite the expression in the form \[5^n\].*

\[\dfrac{5^{10}}{5^{12}}=\]

To rewrite the expression \(\dfrac{5^{10}}{5^{12}}\) in the form \(5^n\), we use the property of exponents:

\[
\dfrac{a^m}{a^n} = a^{m-n}
\]

where \(a = 5\), \(m = 10\), and \(n = 12\).

Applying this rule:

\[
\dfrac{5^{10}}{5^{12}} = 5^{10 - 12}
\]

Calculating the exponent:

\[
5^{10 - 12} = 5^{-2}
\]

So, the expression \(\dfrac{5^{10}}{5^{12}}\) rewritten in the form \(5^n\) is:

\[
\boxed{5^{-2}}
\]

### Would you like more details or have any questions?

### Related Questions:
1. How do you express \(\dfrac{2^{8}}{2^{5}}\) in the form \(2^n\)?
2. What is the value of \(10^{-3}\) and how do you interpret negative exponents?
3. How would you simplify \(5^3 \times 5^{-5}\)?
4. Can you show how to use exponents to simplify expressions with multiplication and division?
5. What is the general rule for raising a power to another power (like \((5^2)^3\))?

**Tip:** Remember, a negative exponent means the reciprocal of the base raised to the corresponding positive exponent.

Learn how to simplify exponents by rewriting the expression \( \frac{5^{10}}{5^{12}} \) in the form \( 5^n \). Understand the division of powers rule and negative exponents. Suitable for students in Grades 6-8.

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