Simplify the following expression. Assume that the variables represent positive real numbers. \( \frac{\left(x^{1 / 5}\right)^{2}}{\left(x^{2}\right)^{7 / 5}} \) \( \frac{\left(x^{1 / 5}\right)^{2}}{\left(x^{2}\right)^{7 / 5}}=\square \) (Type exponential notation with positive exponents. Simplify your answer. Use integers or fractions for any numbers in the expression.)

Let's simplify the expression step by step. Starting with the given expression: \[ \frac{\left(x^{1 / 5}\right)^{2}}{\left(x^{2}\right)^{7 / 5}} \] We simplify the numerator first: \[ \left(x^{1 / 5}\right)^{2} = x^{(1/5) \cdot 2} = x^{2/5} \] Next, we simplify the denominator: \[ \left(x^{2}\right)^{7 / 5} = x^{2 \cdot (7/5)} = x^{14/5} \] Now, we can rewrite the expression: \[ \frac{x^{2/5}}{x^{14/5}} \] Using the property of exponents \( \frac{a^m}{a^n} = a^{m-n} \), we get: \[ x^{(2/5) - (14/5)} = x^{(2 - 14)/5} = x^{-12/5} \] Since we need positive exponents, we can express \(x^{-12/5}\) as: \[ \frac{1}{x^{12/5}} \] Thus, the simplified expression is: \[ \frac{1}{x^{12/5}} \] Final Output: \(\frac{1}{x^{12 / 5}}\)