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​(Type exponential notation with positive​ exponents.)

The given expression is:

\[
\frac{p^3}{p^{15}}
\]

To simplify, we apply the rule for dividing exponents with the same base, which states that:

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

Here, \( m = 3 \) and \( n = 15 \), so we subtract the exponents:

\[
p^{3 - 15} = p^{-12}
\]

To express this with a positive exponent, we write:

\[
p^{-12} = \frac{1}{p^{12}}
\]

Thus, the simplified expression is:

\[
\frac{1}{p^{12}}
\]

Let me know if you need more details or have any questions! Here are 5 related questions for you to try:

1. Simplify \(\frac{x^5}{x^9}\).
2. Simplify \(\frac{y^{10}}{y^2}\).
3. Simplify \(\frac{a^7}{a^4}\).
4. Express \(b^{-3}\) as a fraction with a positive exponent.
5. Simplify \(\frac{m^8}{m^3}\).

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

Learn how to simplify the exponential expression p^3 divided by p^15. This problem teaches the exponent subtraction rule and shows how to express negative exponents in positive form. Ideal for students in Grades 7-9.

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