Question

Find the term independent of $x$ in the expansion of ${[\frac{1}{2}{x}^{1/3}+x^{-1/5}]}^8$

• A. $T_3$
• B. $T_5$
• C. $T_6$
• D. $T_8$

Answer 1

The correct option is C $T_6$

We know that the expansion of $(\frac{1}{2}{x}^{\frac{1}{3}}+x^{\frac{-1}{5}})$ will have term $\left(x^{\frac{1}{3}}{)}^{8-b}\right(x^{\frac{-1}{5}}{)}^b$
We want the power of x to be 0,
$=>\frac{(8-b)}{3}-\frac{b}{5}=0=5(8-b)-3b$
$=>8b=40=>b=5$ , so the term is $T_6$