IB Mathematics Analysis and Approaches Question Type 2: Rewriting Equations Using Rational Exponents Exercises

Rewrite $(\sqrt[5]{y^2}{)}^{-3}$ as a single power of $y$.

Simplify $\frac{x^{\frac{3}{4}}\cdot x^{\frac{1}{6}}}{x^{\frac{1}{2}}}$ and express the result as $x^k$.

Simplify $(x^{2/3}{y}^{-1/4}{)}^{-3/2}$ and express the result with positive rational exponents.

Simplify ${\left(\frac{\sqrt{x^{2}y}}{y^{1/4}}\right)}^{-2}$ giving your answer with positive rational exponents.

Simplify ${\left(\frac{x^{-1/2}{y}^{3/4}}{x^{1/3}{y}^{-2/3}}\right)}^{-3/2}$, giving your answer with positive rational exponents.

Simplify $(x^{-1/2}{y}^{1/3}{)}^{-2}$, expressing the result with positive rational exponents.

Rewrite ${\left(\sqrt[3]{\frac{1}{x}}\right)}^2$ using rational exponents. [2]

Express $\sqrt[3]{\sqrt{x}}$ in the form $x^p$ with a rational $p$.

Rewrite $\sqrt[3]{x^2}$ using a rational exponent. [1]

Express $x^{-7/5}$ in radical notation.

Simplify $(\sqrt[4]{x^3}{)}^2$ using rational exponents. [2 marks]

Rewrite and simplify ${\left(\sqrt[3]{x}\cdot \sqrt[6]{x^2}\right)}^3$ in simplest form.

Express $\frac{\sqrt{x}}{\sqrt[3]{x^2}}$ as a single power of $x$.

Express $(\sqrt{x}{)}^4$ using rational exponents.