To simplify the expression [tex]\( n^{-6} p^3 \)[/tex], let's go through the steps methodically:
1. Understand Negative Exponents:
- A negative exponent indicates that the base should be moved to the denominator with a positive exponent. Specifically, [tex]\( n^{-6} \)[/tex] can be rewritten as [tex]\( \frac{1}{n^6} \)[/tex].
2. Rewrite the Expression:
- Given [tex]\( n^{-6} p^3 \)[/tex], we can separate it:
[tex]\[
n^{-6} p^3 = \left(\frac{1}{n^6}\right) p^3
\][/tex]
3. Combine the Terms:
- When multiplying two expressions, one of which is a fraction, you multiply the numerators and then the denominators separately. This yields:
[tex]\[
\left(\frac{1}{n^6}\right) p^3 = \frac{1 \cdot p^3}{n^6 \cdot 1} = \frac{p^3}{n^6}
\][/tex]
Thus, the simplified form of [tex]\( n^{-6} p^3 \)[/tex] is:
[tex]\[
\frac{p^3}{n^6}
\][/tex]
So, the correct option is:
[tex]\[
\boxed{\frac{p^3}{n^6}}
\][/tex]
