Identify the simplified form of the expression%C2%A0 r−7+p−12 .(1 point) Responses r7p12 the fraction with numerator r to the 7th power and denominator p to the 12th power −r7−p12 negative r to the 7th power minus p to the 12th power 1r7p12 the fraction with numerator 1 and denominator r to the 7th power p to the 12th power 1r7+1p12

Answer 1

To simplify the expression \( r^{-7} + p^{-12} \):

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

Thus, we can express the original expression as:

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

This means the expression does not simplify to a single fraction without a common denominator.

However, from the options given:

• \( r^7 p^{12} \) is incorrect as it does not represent the original expression.
• \( -r^7 - p^{12} \) is incorrect since the original expression is not negative.
• \( \frac{1}{r^{7} p^{12}} \) is also incorrect as it represents a product rather than a sum.
• \( \frac{1}{r^7} + \frac{1}{p^{12}} \) is the correct representation but is not listed explicitly among the options.

If we stick strictly to the provided answer choices, the most appropriate pick is:

1. \( \frac{1}{r^7} + \frac{1}{p^{12}} \) (not explicitly listed).

If you need to choose one from the list, none of the options directly match the simplified form of \( r^{-7} + p^{-12} \).