Question

which is the simplified form of \\(r^{-7} + s^{-12}\\)?

\\(\circ\quad \frac{1}{r^7 s^{12}}\\)

\\(\circ\quad -r^7 - s^{12}\\)

\\(\circ\quad \frac{r^7}{s^{12}}\\)

\\(\circ\quad \frac{1}{r^7} + \frac{1}{s^{12}}\\)

Explanation:

Apply the negative exponent rule

$$ x^{-n} = \frac{1}{x^n} $$

Rewrite each term individually

$$ r^{-7} = \frac{1}{r^7} $$

$$ s^{-12} = \frac{1}{s^{12}} $$

Combine the rewritten terms

$$ r^{-7} + s^{-12} = \frac{1}{r^7} + \frac{1}{s^{12}} $$

Answer:

• (A) \(\frac{1}{r^7 s^{12}}\)
• (B) \(-r^7 - s^{12}\)
• (C) \(\frac{r^7}{s^{12}}\)
• (D) \(\frac{1}{r^7} + \frac{1}{s^{12}}\) (Correct answer)