Question Type 8: Finding corresponding coefficients for fractional, multi-powered binomials Exercises

Find the coefficient of $x^6$ in $\left(\frac{1}{3x} + 2x^2\right)^9$.

Find the coefficient of $x^3$ in $\left(2x^2 + \frac{3}{x}\right)^6$.

Find the coefficient of $x^5$ in $(2\sqrt{x} + 3x^{3/2})^6$.

Find the coefficient of $x^2$ in $(\frac{5}{x^2} + 4x^4)^5$.

Find the coefficient of $x$ in $\left(\frac{4}{x} + 5x^2\right)^5$.

Find the coefficient of $x^{10}$ in $\left(\frac{3}{x} + 2x^2\right)^8$.

Find the coefficient of $x^5$ in $(x^{-1} + 2x^3)^7$.

Find the coefficient of $x^4$ in $(3\sqrt{x} + 2x^2)^5$.

Find the coefficient of $x^4$ in $\left(\frac{1}{x} + x^3\right)^4$.

Find the coefficient of $x^5$ in $\left(\frac{1}{2} x^{2/3} - x^{-1/3}\right)^9$.

Find the coefficient of $x^7$ in $\left(3x^2 + \frac{1}{2x}\right)^8$.