\( \frac{\left(2 a^{5} b\right)^{2}}{24 b^{6}} \) Oa. \( \frac{a^{10} b^{4}}{6} \quad \) Ob. \( \frac{a^{10}}{12 b^{4}} \) O. \( \frac{a^{7}}{6 b^{4}} \) Od. \( \frac{a^{10}}{6 b^{4}} \)

To simplify \( \frac{\left(2 a^{5} b\right)^{2}}{24 b^{6}} \), let's start with the numerator: \[ \left(2 a^{5} b\right)^{2} = 4 a^{10} b^{2} \] Now substitute this back into the expression: \[ \frac{4 a^{10} b^{2}}{24 b^{6}} \] Now simplify the fraction by dividing the coefficients: \[ \frac{4}{24} = \frac{1}{6} \] Now for the variables, we have: \[ \frac{a^{10} b^{2}}{b^{6}} = a^{10} b^{2 - 6} = a^{10} b^{-4} \] Putting this all together, we get: \[ \frac{a^{10}}{6 b^{4}} \] So the final simplified expression is: \[ \frac{a^{10}}{6 b^{4}} \] The correct answer is: **Od.** \( \frac{a^{10}}{6 b^{4}} \)