IB Mathematics Applications & Interpretation Question Type 2: Simplifying Algebraic Expressions Involving Rational Exponents Exercises

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

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

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

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

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

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

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

Simplify the expression: $${\left(\frac{x^{4/5}{y}^{2/5}}{x^{1/5}{y}^{3/5}}\right)}^{5/2}$$ giving your answer with positive exponents.

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

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

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

Simplify the expression $27^{2/3}\cdot 9^{1/2}$.