IB Mathematics Analysis and Approaches Question Type 8: Finding Corresponding Coefficients for Fractional, Multi-powered Binomials Exercises

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

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 ${\left(3x^2+\frac{1}{2x}\right)}^8$.