Question

Identify the simplified form of the expression r−7+p−12 .(1 point)Responses1r7p12the fraction with numerator 1 and denominator r to the 7th power p to the 12th power1r7+1p12the fraction with numerator 1 and denominator r to the 7th power plus the fraction with numerator 1 and denominator p to the 12th powerr7p12the fraction with numerator r to the 7th power and denominator p to the 12th power−r7−p12

Answer 1

To simplify the expression \( r^{-7} + p^{-12} \), we can rewrite it using the properties of exponents.

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

So, the expression becomes:

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

This implies that the expression does not simplify further into a single fraction unless you have a common denominator.

Therefore, the simplest form of the expression \( r^{-7} + p^{-12} \) is:

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

Among the provided choices, if we need to select the one that matches this expression, we look for the choice that correctly represents the fractions. The corresponding choice would need to be:

1/r^7 + 1/p^12 (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).