To simplify the expression [tex]\( r^{-7} + s^{-12} \)[/tex]:
1. Understand negative exponents:
- A negative exponent indicates the reciprocal of the base raised to the corresponding positive exponent.
- Thus, [tex]\( r^{-7} \)[/tex] can be rewritten as [tex]\( \frac{1}{r^7} \)[/tex].
- Similarly, [tex]\( s^{-12} \)[/tex] can be rewritten as [tex]\( \frac{1}{s^{12}} \)[/tex].
2. Rewrite the terms using positive exponents:
- [tex]\( r^{-7} = \frac{1}{r^7} \)[/tex]
- [tex]\( s^{-12} = \frac{1}{s^{12}} \)[/tex]
3. Combine the simplified terms:
- Add the two terms together to get [tex]\( \frac{1}{r^7} + \frac{1}{s^{12}} \)[/tex].
Thus, the simplified form of [tex]\( r^{-7} + s^{-12} \)[/tex] is:
[tex]\[
\frac{1}{r^7} + \frac{1}{s^{12}}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{1}{r^7} + \frac{1}{s^{12}}}
\][/tex]
