Simplify (2x^3)^(1/2)+x^(4/3)-x^-1

${(2 x^{3})}^{\frac{1}{2}} + x^{\frac{4}{3}} - x^{- 1}$

Apply the product rule to $2 x^{3}$ .

$2^{\frac{1}{2}} {(x^{3})}^{\frac{1}{2}} + x^{\frac{4}{3}} - x^{- 1}$

Multiply the exponents in ${(x^{3})}^{\frac{1}{2}}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2^{\frac{1}{2}} x^{3 (\frac{1}{2})} + x^{\frac{4}{3}} - x^{- 1}$

Combine $3$ and $\frac{1}{2}$ .

$2^{\frac{1}{2}} x^{\frac{3}{2}} + x^{\frac{4}{3}} - x^{- 1}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$2^{\frac{1}{2}} x^{\frac{3}{2}} + x^{\frac{4}{3}} - \frac{1}{x}$