(1) Simplify a, \( \frac{8 x^{3} y^{3}}{24 x^{5} y^{2}} \) \( \frac{\left(2 a^{2} b\right)^{3}\left(2^{3} a b^{2}\right)}{\left(2^{5} a^{4} b^{3}\right)} \)

Let’s dive into simplifying the two expressions! First up, for \( \frac{8 x^{3} y^{3}}{24 x^{5} y^{2}} \), we simplify the coefficients and the variables separately. The coefficient simplifies to \( \frac{8}{24} = \frac{1}{3} \). For the variables, \( x^{3}/x^{5} = x^{3-5} = x^{-2} \) and \( y^{3}/y^{2} = y^{3-2} = y^{1} \). So, combined, the result is \( \frac{1}{3} \cdot y \cdot \frac{1}{x^{2}} = \frac{y}{3 x^{2}} \). Next, for \( \frac{\left(2 a^{2} b\right)^{3}\left(2^{3} a b^{2}\right)}{\left(2^{5} a^{4} b^{3}\right)} \), we first deal with the numerator: \( \left(2 a^{2} b\right)^{3} = 2^{3} (a^{2})^{3} (b)^{3} = 8 a^{6} b^{3} \) and \( 2^{3} a b^{2} = 8 a b^{2} \). Thus, \( 8 a^{6} b^{3} \times 8 a b^{2} = 64 a^{7} b^{5} \). In the denominator, \( 2^5 a^4 b^3 = 32 a^4 b^3 \). The division gives us \( \frac{64 a^{7} b^{5}}{32 a^{4} b^{3}} = 2 a^{7-4} b^{5-3} = 2 a^{3} b^{2} \). So, the simplified forms are: 1. \( \frac{y}{3 x^{2}} \) 2. \( 2 a^{3} b^{2} \)