Identify the simplified form of the expression r−7+p−12

Question

.(1 point)
Responses

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

r7p12
the 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 apply the rule of exponents, which states that \( a^{-n} = \frac{1}{a^n} \).

Thus, we can rewrite the expression as:

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

This means the simplified version of your expression can either be the two terms separated:

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

However, if you need just the single form, the most appropriate choice from your options is:

\( -r^{7} - p^{12} \) (since that is the only option that changes the signs correctly).

If you need to combine them more simply, you would normally write \( \frac{1}{r^7} + \frac{1}{p^{12}} \), indicating both terms are fractions.

Here's how we would analyze your choices specifically:

1. \( \frac{1}{r^7 p^{12}} \) does not seem accurate since it suggests a multiplication of denominators rather than addition.
2. \( 1/r^7 + 1/p^{12} \) is indeed correct.
3. \( r^{7}/p^{12} \) does not accurately reflect the original expression.
4. \( -r^{7} - p^{12} \) implies a different operation (a combination of negative excess rather than reciprocating the bases).

Thus, the best choice from your options is \( \frac{1}{r^7} + \frac{1}{p^{12}} \).