Which is equivalent to \( \sqrt[5]{1,215}^{x} \) ? \( 243^{x} \) \( 1,215^{\frac{1}{5} x} \) \( 1,215^{\frac{1}{5 x}} \) \( 243^{\frac{1}{x}} \)

To determine which expression is equivalent to \( \sqrt[5]{1,215}^{x} \), we start by rewriting the expression. The fifth root can be expressed as an exponent: \[ \sqrt[5]{1,215} = 1,215^{\frac{1}{5}}. \] Now, raising this to the power \( x \) gives us: \[ \sqrt[5]{1,215}^{x} = \left(1,215^{\frac{1}{5}}\right)^{x} = 1,215^{\frac{x}{5}}. \] Now, let's analyze the provided options. The second option, \( 1,215^{\frac{1}{5} x} \), is the same as \( 1,215^{\frac{x}{5}} \), confirming that it is indeed equivalent. Thus, the correct answer is: \( 1,215^{\frac{1}{5} x} \).