Question

which expression is equivalent to \\((r^{-7})^6\\)?

\\(r^{42}\\)

\\(\frac{1}{r^{42}}\\)

\\(-7r^6\\)

\\(\frac{1}{r}\\)

Explanation:

Apply the power of a power rule

Using the Exponent Rules knowledge point

$$ (r^{-7})^6 = r^{-7 \cdot 6} = r^{-42} $$

Simplify the negative exponent

Using the Negative Exponents knowledge point

$$ r^{-42} = \frac{1}{r^{42}} $$

Answer:

• (A) \(r^{42}\)
• (B) \(\frac{1}{r^{42}}\) (Correct answer)
• (C) \(-7r^6\)
• (D) \(\frac{1}{r}\)