Another exponent rule states that \((mn)^p = m^p n^p\). For example, \((3x)^2 = 3^2 x^2 = 9x^2\), and \((xyz^2)^3 = x^3 y^3 (z^2)^3 = x^3 y^3 z^6\).

Use this rule to show why \(\sqrt[3]{x^3 y^6 z^4} = xy^2z\sqrt[3]{z}\), by converting each side of the equation to its exponential form.

Use exponent rules to show that the equations are true.

1. $x \sqrt{x} = x^\frac{3}{2}$
2. $\sqrt[3]{y^9} = y^3$
3. $\frac{z}{\sqrt{z}} = \sqrt{z}$