Question

which expression is equivalent to the given expression? \\((3m^{-4})^{3}(3m^{6})\\) \\(\bigcirc\\) a. \\(\frac{81}{m^{3}}\\) \\(\bigcirc\\) b. \\(\frac{27}{m^{7}}\\) \\(\bigcirc\\) c. \\(\frac{27}{m^{3}}\\) \\(\bigcirc\\) d. \\(\frac{81}{m^{7}}\\)

Explanation:

Step1: Expand the power of product

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

Step2: Multiply with the second term

$27m^{-12} \cdot 3m^6 = (27 \times 3) \cdot m^{-12+6} = 81m^{-6}$

Step3: Rewrite negative exponent

$81m^{-6} = \frac{81}{m^6}$

Answer:

A. $\frac{81}{m^6}$