# How do you simplify root3( y^4)?

Jul 1, 2016

$y \textcolor{w h i t e}{.} \sqrt[3]{y}$

#### Explanation:

${y}^{4}$ is the same as $y \times y \times y \times y$

So we are able to group this into

$\left(y \times y \times y\right) \times y$ which is the same as ${y}^{3} \times y$

Write $\sqrt[3]{{y}^{4}} \text{ }$ as $\text{ } \sqrt[3]{{y}^{3} \times y}$

We can take the ${y}^{3}$ outside the cube root but in doing so it becomes just $y$

So $\sqrt[3]{{y}^{4}} \text{ "=" "root(3)(y^3xxy)" "=" } y \textcolor{w h i t e}{.} \sqrt[3]{y}$
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Just for information: another way of writing $\sqrt[3]{{y}^{4}} \text{ is } {y}^{\frac{4}{3}}$