Question Type 2: Simplifying algebraic expressions involving rational exponents Exercises

Simplify the expression $x^{1/2}\cdot x^{1/3}$ and express your answer as a single power of $x$.

Simplify the expression $27^{2/3}\cdot9^{1/2}$.

Simplify the expression $(\sqrt[3]{x^2})^{-3}$ and express your answer using positive rational exponents.

Simplify the expression $\sqrt{x}\cdot\sqrt[3]{x^2}$ and express your answer as a single power of $x$.

Simplify the expression $\dfrac{16^{3/4}}{8^{1/3}}$.

Simplify the expression $\left(\dfrac{x^{2/3}}{x^{1/6}}\right)^3$.

Simplify the expression $(x^3y^{-2})^{2/3}$.

Simplify the expression $\dfrac{8x^{3/2}y^{-1/2}}{2x^{1/2}y^{1/2}}$.

Simplify the expression $(x^{-1/2}y^{1/3})^{-3}$.

Simplify the expression $\dfrac{(2x^{1/4}y^{1/2})^4}{8xy^2}$.

Simplify the expression $(64a^{-2}b^3)^{2/3}$.

Simplify the expression $\left(\dfrac{x^{4/5}y^{2/5}}{x^{1/5}y^{3/5}}\right)^{5/2}$.