Question

which expression is equivalent to the given expression?
\\((3m^{-4})^3(3m^5)\\)

• \\(\frac{9}{m^7}\\)
• \\(\frac{27}{m^7}\\)
• \\(\frac{27}{m^2}\\)
• \\(\frac{81}{m^7}\\)

Explanation:

Simplify the first term using the power of a product rule

$$ (3m^{-4})^3 = 3^3 \cdot (m^{-4})^3 = 27 \cdot m^{-12} $$

Multiply the simplified term by the second term

$$ (27m^{-12}) \cdot (3m^5) = (27 \cdot 3) \cdot (m^{-12} \cdot m^5) = 81 \cdot m^{-12 + 5} = 81m^{-7} $$

Rewrite the expression with positive exponents

$$ 81m^{-7} = \frac{81}{m^7} $$

Answer:

• (A) \(\frac{9}{m^7}\)
• (B) \(\frac{27}{m^7}\)
• (C) \(\frac{27}{m^{12}}\)
• (D) \(\frac{81}{m^7}\) (Correct answer)