How do you simplify (x^(1/pi)/y^(2/pi))^pi?

3 Answers
Jul 21, 2018

(x^(1/pi) / y^(2/pi))^pi = x / y^2

Explanation:

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

(a^b)^c = a^(bc)

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

(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

Jul 21, 2018

x/y^2

Explanation:

(x^(1/pi)/y^(2/pi))^pi=x^(pi/pi)/y^((2pi)/pi)=x/y^2

\frac{x}{y^2}

Explanation:

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

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

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

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

=\frac{x}{y^2}