How do you simplify $\sqrt[3]{y^{4}}$ $root3( y^4)$ ?

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How do you simplify $\sqrt[3]{y^{4}}$ $root3( y^4)$ ?

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Answer 1 · 2016-07-01T21:38:33

$y . \sqrt[3]{y}$ $ycolor(white)(.) root(3)(y)$

Explanation:

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

So we are able to group this into

$(y \times y \times y) \times y$ $(yxxyxxy)xxy$ which is the same as $y^{3} \times y$ $y^3xxy$

Write $\sqrt[3]{y^{4}}$ $root(3)(y^4)" "$ as $\sqrt[3]{y^{3} \times y}$ $" "root(3)(y^3xxy)$

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

So $\sqrt[3]{y^{4}} = \sqrt[3]{y^{3} \times y} = y . \sqrt[3]{y}$ $root(3)(y^4)" "=" "root(3)(y^3xxy)" "=" "ycolor(white)(.) root(3)(y)$
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Just for information: another way of writing $\sqrt[3]{y^{4}} is y^{\frac{4}{3}}$ $root(3)(y^4)" is "y^(4/3)$

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How do you simplify $\sqrt[3]{y^{4}}$ $root3( y^4)$ ?

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