Find the indicated term of the binomial expansion.
-6th term; $\left( \frac { 4 } { m ^ { 3 } } + \frac { m ^ { 2 } } { 8 } \right) ^ { 8 }$
A) $\frac { 896 } { m ^ { 9 } }$
B) $\frac { 112 } { \mathrm {~m} ^ { 9 } }$
C) $\frac { 7 m ^ { 9 } } { 16 }$
D) $\frac { 56 m ^ { 9 } } { 16 }$

Question

Quizplus · Accepted Answer

The 6th term in the expansion of $\left( a + b \right)^n$ is given by $T_{k+1} = \binom{n}{k} a^{n-k} b^k$, where $k = 5$ for the 6th term. Here, $a = \frac{4}{m^3}$, $b = \frac{m^2}{8}$, and $n = 8$. Thus, $T_6 = \binom{8}{5} \left(\frac{4}{m^3}\right)^{3} \left(\frac{m^2}{8}\right)^{5} = 56 \cdot \frac{64}{m^9} \cdot \frac{m^{10}}{32768} = \frac{56 \cdot 64 \cdot m}{32768 \cdot m^9} = \frac{112}{m^9}$.

Find the Indicated Term of the Binomial Expansion (4m3+m28)8\left( \frac { 4 } { m ^ { 3 } } + \frac { m ^ { 2 } } { 8 } \right) ^ { 8 }(m34​+8m2​)8

Find the Indicated Term of the Binomial Expansion $\left( \frac { 4 } { m ^ { 3 } } + \frac { m ^ { 2 } } { 8 } \right) ^ { 8 }$