Question

Identify the simplified form of the expression r−4p−8
.(1 point)
Responses

1r4p8
the fraction with numerator 1 and denominator r to the 4th power p to the 8th power

−r4−p8
negative r to the 4th power minus p to the 8th power

1r4+1p8
the fraction with numerator 1 and denominator r to the 4th power plus the fraction with numerator 1 and denominator p to the 8th power

r4p8

Answer 1

To simplify the expression \( r^{-4} p^{-8} \), we can rewrite it in terms of positive exponents.

Using the rule that \( x^{-n} = \frac{1}{x^n} \), we have:

\[
r^{-4} = \frac{1}{r^4}
\]
\[
p^{-8} = \frac{1}{p^8}
\]

Therefore, the expression can be rewritten as:

\[
r^{-4} p^{-8} = \frac{1}{r^4} \cdot \frac{1}{p^8} = \frac{1}{r^4 p^8}
\]

So, the simplified form of the expression \( r^{-4} p^{-8} \) is:

\[
\frac{1}{r^4 p^8}
\]

The correct answer from the options given is: **the fraction with numerator 1 and denominator r to the 4th power p to the 8th power.**