How do you simplify ${(\frac{x^{\frac{1}{π}}}{y^{\frac{2}{π}}})}^{π}$ $(x^(1/pi)/y^(2/pi))^pi$ ?

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How do you simplify ${(\frac{x^{\frac{1}{π}}}{y^{\frac{2}{π}}})}^{π}$ $(x^(1/pi)/y^(2/pi))^pi$ ?

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Answer 1 · 2018-07-21T07:08:14

${(\frac{x^{\frac{1}{π}}}{y^{\frac{2}{π}}})}^{π} = \frac{x}{y^{2}}$ $(x^(1/pi) / y^(2/pi))^pi = x / y^2$

Explanation:

Note that if $a > 0$ $a > 0$ and $b, c$ $b, c$ are any real numbers then:

${(a^{b})}^{c} = a^{b c}$ $(a^b)^c = a^(bc)$

So (assuming $x, y > 0$ $x, y > 0$ ) we find:

${(\frac{x^{\frac{1}{π}}}{y^{\frac{2}{π}}})}^{π} = \frac{{(x^{\frac{1}{π}})}^{π}}{{(y^{\frac{2}{π}})}^{π}} = \frac{x^{\frac{1}{π} \cdot π}}{y^{\frac{2}{π} \cdot π}} = \frac{x}{y^{2}}$ $(x^(1/pi) / y^(2/pi))^pi = (x^(1/pi))^pi / (y^(2/pi))^pi = (x^(1/pi * pi)) / (y^(2/pi * pi)) = x / y^2$

Answer 2 · 2018-07-21T12:37:39

$\frac{x}{y^{2}}$ $x/y^2$

Explanation:

${(\frac{x^{\frac{1}{π}}}{y^{\frac{2}{π}}})}^{π} = \frac{x^{\frac{π}{π}}}{y^{\frac{2 π}{π}}} = \frac{x}{y^{2}}$ $(x^(1/pi)/y^(2/pi))^pi=x^(pi/pi)/y^((2pi)/pi)=x/y^2$

Answer 3 · 2018-07-21T13:55:03

$\frac{x}{y^{2}}$ $\frac{x}{y^2}$

Explanation:

${(\frac{x^{\frac{1}{π}}}{y^{\frac{2}{π}}})}^{π}$ $(\frac{x^{1/\pi}}{y^{2/\pi}})^\pi$

$= \frac{{(x^{\frac{1}{π}})}^{π}}{{(y^{\frac{2}{π}})}^{π}}$ $=\frac{(x^{1/\pi})^\pi}{(y^{2/\pi})^\pi$

$= \frac{x^{π \cdot \frac{1}{π}}}{y^{π \cdot \frac{2}{π}}}$ $=\frac{x^{\pi\cdot 1/\pi}}{y^{\pi\cdot 2/\pi}$

$= \frac{x^{1}}{y^{2}}$ $=\frac{x^1}{y^2}$

$= \frac{x}{y^{2}}$ $=\frac{x}{y^2}$

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How do you simplify ${(\frac{x^{\frac{1}{π}}}{y^{\frac{2}{π}}})}^{π}$ $(x^(1/pi)/y^(2/pi))^pi$ ?

3 Answers

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