Question

Identify the simplified form of the expression r−7+p−12
.(1 point)
Responses

1r7p12
the fraction with numerator 1 and denominator r to the 7th power p to the 12th power

r7p12
the fraction with numerator r to the 7th power and denominator p to the 12th power

1r7+1p12
the fraction with numerator 1 and denominator r to the 7th power plus the fraction with numerator 1 and denominator p to the 12th power

−r7−p12
negative r to the 7th power minus p to the 12th power

Answer 1

To simplify the expression \( r^{-7} + p^{-12} \), we can rewrite it in terms of positive exponents:

1. \( r^{-7} \) can be expressed as \( \frac{1}{r^7} \).
2. \( p^{-12} \) can be expressed as \( \frac{1}{p^{12}} \).

Thus, the expression becomes:

\[
\frac{1}{r^7} + \frac{1}{p^{12}}
\]

However, it can also be left in its original form \( r^{-7} + p^{-12} \) since that is a simplified version as well.

From the provided options, the correct response that matches our simplification is:

**1/r^7 + 1/p^12**

This indicates the sum of the fractions with the respective denominators:

So the correct answer is:
- **1/r7 + 1/p12**