Simplify the following expression. Assume that all variables represent positive real numbers. Give your answer in terms of positive exponents. \( \frac{m^{\frac{3}{4}} n^{\frac{-1}{4}}}{\left(m^{2} n\right)^{\frac{1}{2}}} \) \( \frac{m^{\frac{3}{4}} n^{\frac{-1}{4}}}{\left(m^{2} n\right)^{\frac{1}{2}}}=\square \) \( ( \) Give your answer in terms of positive exponents.)

First, let's simplify the expression step by step. The denominator \((m^{2} n)^{\frac{1}{2}}\) can be simplified using the power of a product rule, where we multiply the exponents: \[ (m^{2} n)^{\frac{1}{2}} = m^{2 \cdot \frac{1}{2}} n^{1 \cdot \frac{1}{2}} = m^{1} n^{\frac{1}{2}} = m n^{\frac{1}{2}}. \] Now, substitute this back into the original expression: \[ \frac{m^{\frac{3}{4}} n^{\frac{-1}{4}}}{m n^{\frac{1}{2}}}. \] Next, simplify this fraction by subtracting the exponents of like bases (using the rule \(a^{m}/a^{n} = a^{m-n}\)): \[ = m^{\frac{3}{4} - 1} n^{\frac{-1}{4} - \frac{1}{2}}. \] Calculating the exponents gives: \[ \frac{3}{4} - 1 = \frac{3}{4} - \frac{4}{4} = \frac{-1}{4}, \] \[ \frac{-1}{4} - \frac{1}{2} = \frac{-1}{4} - \frac{2}{4} = \frac{-3}{4}. \] Thus, we have: \[ m^{\frac{-1}{4}} n^{\frac{-3}{4}}. \] To express everything in terms of positive exponents, we can rewrite: \[ = \frac{1}{m^{\frac{1}{4}} n^{\frac{3}{4}}}. \] So, the simplified expression in terms of positive exponents is: \[ \frac{1}{m^{\frac{1}{4}} n^{\frac{3}{4}}} = \square. \]