Simplify the exponential expression. \( \left(\frac{-35 a^{5} b^{7}}{7 a^{7} b^{-2}}\right)^{3} \) \( \left(\frac{-35 a^{5} b^{7}}{7 a^{7} b^{-2}}\right)^{3}=\square \) (Simplify your answer. Use positive exponents only.)

First, let's simplify the expression inside the parentheses: \[ \frac{-35 a^{5} b^{7}}{7 a^{7} b^{-2}} = \frac{-35}{7} \cdot \frac{a^{5}}{a^{7}} \cdot \frac{b^{7}}{b^{-2}} \] Calculating each part: \[ \frac{-35}{7} = -5 \] \[ \frac{a^{5}}{a^{7}} = a^{5-7} = a^{-2} \] \[ \frac{b^{7}}{b^{-2}} = b^{7 - (-2)} = b^{7 + 2} = b^{9} \] Putting it all together, we have: \[ \frac{-35 a^{5} b^{7}}{7 a^{7} b^{-2}} = -5 a^{-2} b^{9} \] Next, we take this simplified form and raise it to the power of 3: \[ (-5 a^{-2} b^{9})^{3} = (-5)^{3} \cdot (a^{-2})^{3} \cdot (b^{9})^{3} \] Calculating each part: \[ (-5)^{3} = -125 \] \[ (a^{-2})^{3} = a^{-6} \] \[ (b^{9})^{3} = b^{27} \] Combining these, we get: \[ (-125) a^{-6} b^{27} \] To express with positive exponents, we rewrite \(a^{-6}\): \[ -125 \frac{b^{27}}{a^{6}} \] Thus, the simplified expression is: \[ \left(\frac{-35 a^{5} b^{7}}{7 a^{7} b^{-2}}\right)^{3} = -\frac{125 b^{27}}{a^{6}} \]