Question

simplify by reducing the index of the radical.
\sqrt35{x^{7}y^{14}}

Explanation:

Step1: Rewrite radical as exponents

$$\sqrt[35]{x^7 y^{14}} = (x^7 y^{14})^{\frac{1}{35}}$$

Step2: Distribute exponent to terms

$$(x^7 y^{14})^{\frac{1}{35}} = x^{7 \times \frac{1}{35}} y^{14 \times \frac{1}{35}}$$

Step3: Simplify exponents

$$x^{\frac{7}{35}} y^{\frac{14}{35}} = x^{\frac{1}{5}} y^{\frac{2}{5}}$$

Step4: Rewrite as single radical

$$x^{\frac{1}{5}} y^{\frac{2}{5}} = \sqrt[5]{x y^2}$$

Answer:

$\sqrt[5]{x y^2}$