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 $\left(\dfrac{\sqrt{x^2y}}{y^{1/4}}\right)^{-2}$ 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.