Question

which is the simplified form of \\( \left(9c^{-9}\
ight)^{-3} \\)?

• \\( 9c^{27} \\)
• \\( \frac{1}{729}c^{27} \\)
• \\( 729c^{27} \\)
• \\( \frac{9}{c^{27}} \\)

Explanation:

Apply the power of a product rule

$$ (9c^{-9})^{-3} = 9^{-3} \cdot (c^{-9})^{-3} $$

Simplify the numerical base with negative exponent

$$ 9^{-3} = \frac{1}{9^3} = \frac{1}{729} $$

Apply the power of a power rule

$$ (c^{-9})^{-3} = c^{-9 \cdot (-3)} = c^{27} $$

Combine the simplified terms

$$ \frac{1}{729}c^{27} $$

Answer:

• (A) \(9c^{27}\)
• (B) \(\frac{1}{729}c^{27}\) (Correct answer)
• (C) \(729c^{27}\)
• (D) \(\frac{9}{c^{27}}\)