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

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

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

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

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

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

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

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

Find the coefficient of $x^{-2}$ in $(7x^{-2} + x^3)^6$.

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

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

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

Find the coefficient of $x^5$ in $(\tfrac12 x^{2/3} - x^{-1/3})^9$.