Simplify the following expression. $$\left( \frac { 2 a ^ { 2 } \cdot a ^ { 3 } \cdot a ^ { 6 } } { 3 a ^ { 3 } \cdot a ^ { 2 } } \right) ^ { 3 }$$
A) $\frac { 8 a ^ { 18 } } { 27 }$
B) $\frac { 8 a ^ { 24 } } { 27 }$
C) $\frac { 2 a ^ { 11 } } { 3 a ^ { 5 } }$
D) $\frac { 2 a ^ { 18 } } { 3 }$
E) $\frac { 8 a ^ { 18 } } { 3 a ^ { 5 } }$

Question

Quizplus · Accepted Answer

First, simplify the expression inside the parentheses by adding the exponents of $a$ in the numerator and subtracting the exponents of $a$ in the denominator: $2a^{2+3+6}/3a^{3+2} = 2a^{11}/3a^{5}$. Then, simplify the fraction: $2/3 \cdot a^{11-5} = 2/3 \cdot a^{6}$. Raising this to the power of 3 gives $(2/3)^3 \cdot a^{6 \cdot 3} = 8/27 \cdot a^{18}$, which matches option A.

Simplify the Following Expression (2a2⋅a3⋅a63a3⋅a2)3\left( \frac { 2 a ^ { 2 } \cdot a ^ { 3 } \cdot a ^ { 6 } } { 3 a ^ { 3 } \cdot a ^ { 2 } } \right) ^ { 3 }(3a3⋅a22a2⋅a3⋅a6​)3

Simplify the Following Expression $\left( \frac { 2 a ^ { 2 } \cdot a ^ { 3 } \cdot a ^ { 6 } } { 3 a ^ { 3 } \cdot a ^ { 2 } } \right) ^ { 3 }$