How do you simplify $\sqrt[4]{\frac{16}{81}}$ $root4(16/81)$ ?

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Answer 1 · 2018-07-15T21:19:45

$\frac{2}{3}$ $2/3$

Note that ${(\frac{2}{3})}^{4} = \frac{16}{81}$ $(2/3)^4=16/81$

Answer 2 · 2018-07-15T21:26:36

$\frac{2}{3}$ $2/3$

$\sqrt[4]{\frac{16}{81}} = \frac{\sqrt[4]{16}}{\sqrt[4]{81}} = \frac{2}{3}$ $root(4)(16/81)=root(4)(16)/root(4)(81)=2/3$

Answer 3 · 2018-07-16T02:36:18

$\Rightarrow \frac{2}{3}$ $color(purple)(=> 2/3$

$\sqrt[4]{\frac{16}{81}}$ $root 4 (16/81)$

${(a^{m})}^{n} = a^{m n}$ $(a ^m)^n = a^(mn)$

$\Rightarrow \sqrt[4]{\frac{2 \cdot 2 \cdot 2 \cdot 2}{3 \cdot 3 \cdot 3 \cdot 3}}$ $=> root 4 ((2 * 2 * 2 * 2) / (3 * 3 * 3 * 3))$

$\Rightarrow \sqrt[4]{\frac{2^{4}}{3^{4}}}$ $=> root 4 (2^4 / 3^4)$

$\Rightarrow {(\frac{2^{4}}{4^{4}})}^{\frac{1}{4}}$ $=> (2^4 / 4^4)^(1/4)$

$\Rightarrow (\frac{2^{\frac{4}{4}}}{3^{\frac{4}{4}}})$ $=> (2^(4/4)/ 3^(4/4))$

$\Rightarrow \frac{2}{3}$ $color(purple)(=> 2/3$

How do you simplify root4(16/81)4√1681root4(16/81)?