which expression is equivalent to $\frac{(a^{2}b^{4}c)^{2}(6a^{3}b)(2c^{5})^{3}}{4a^{6}b^{12}c^{3}}$?\n$\frac…

which expression is equivalent to $\frac{(a^{2}b^{4}c)^{2}(6a^{3}b)(2c^{5})^{3}}{4a^{6}b^{12}c^{3}}$?\n$\frac{3ac^{7}}{b^{5}}$\n$\frac{9ac^{14}}{b^{3}}$\n$\frac{12ac^{14}}{b^{3}}$\n$\frac{9ac^{7}}{b^{5}}$

which expression is equivalent to $\frac{(a^{2}b^{4}c)^{2}(6a^{3}b)(2c^{5})^{3}}{4a^{6}b^{12}c^{3}}$?\n$\frac{3ac^{7}}{b^{5}}$\n$\frac{9ac^{14}}{b^{3}}$\n$\frac{12ac^{14}}{b^{3}}$\n$\frac{9ac^{7}}{b^{5}}$

Answer

Explanation:

Step1: Expand numerator terms

First, expand ((a^{2}b^{4}c)^{2}=a^{2\times2}b^{4\times2}c^{2}=a^{4}b^{8}c^{2}), ((2c^{5})^{3}=2^{3}c^{5\times3}=8c^{15}). Then the numerator is (a^{4}b^{8}c^{2}\times6a^{3}b\times8c^{15}=6\times8a^{4 + 3}b^{8+1}c^{2 + 15}=48a^{7}b^{9}c^{17}).

Step2: Simplify the fraction

The original expression (\frac{48a^{7}b^{9}c^{17}}{4a^{6}b^{12}c^{3}}). Using the rule (\frac{x^{m}}{x^{n}}=x^{m - n}), we have (\frac{48}{4}a^{7-6}b^{9 - 12}c^{17-3}=12a^{1}b^{- 3}c^{14}=\frac{12ac^{14}}{b^{3}}).

Answer:

(\frac{12ac^{14}}{b^{3}})