Practice section 2 of 8

Simplify the following: (a) $\dfrac{8^{1/3}\cdot27^{-1/2}}{3^{-1/6}\cdot9^{1/3}}$; (b) $\dfrac{x^{1/3}+x^{-2/3}}{x^{4/3}}$.

Solve the equation $4^{x+1}=2-7(2^x)$.

Solve the equation $\log_2x=-1$.

Solve the equation $\log_3x+\log_9x=6$.

Solve the equation $2^x\cdot7^x=9^{x+1}$.

Express $\dfrac{2x+3}{(x+1)(x-1)(2x+1)}$ in partial fractions.