(a) \( \sqrt{288}-\sqrt{18} \) (b) \( \left(9 a^{3} b^{3}\right)\left(3 a b^{2}\right)^{2} \) (c) \( \left(\frac{16 x^{9} y^{3}}{x y^{11}}\right)^{-1 / 2} \) (bimplify each expression. Write your final answer without negative exponents. (a)

To simplify \( \sqrt{288}-\sqrt{18} \), we start by breaking each square root down: 1. For \( \sqrt{288} \), we can express it as \( \sqrt{144 \cdot 2} = 12\sqrt{2} \). 2. For \( \sqrt{18} \), we have \( \sqrt{9 \cdot 2} = 3\sqrt{2} \). Now we can subtract these: \[ 12\sqrt{2} - 3\sqrt{2} = (12 - 3)\sqrt{2} = 9\sqrt{2}. \] So, the final answer for (a) is \( 9\sqrt{2} \). (b) For \( \left(9 a^{3} b^{3}\right)\left(3 a b^{2}\right)^{2} \): 1. Start by simplifying the second part: \[ (3ab^{2})^{2} = 3^{2} (a^{1})^{2} (b^{2})^{2} = 9 a^{2} b^{4}. \] 2. Now we can multiply the terms: \[ 9 a^{3} b^{3} \cdot 9 a^{2} b^{4} = 81 a^{3 + 2} b^{3 + 4} = 81 a^{5} b^{7}. \] Thus, the final answer for (b) is \( 81 a^{5} b^{7} \). (c) To simplify \( \left(\frac{16 x^{9} y^{3}}{x y^{11}}\right)^{-1 / 2} \): 1. First, simplify the inside: \[ \frac{16 x^{9} y^{3}}{xy^{11}} = 16 x^{9-1} y^{3-11} = 16 x^{8} y^{-8}. \] 2. Next, take the reciprocal and apply the exponent: \[ (16 x^{8} y^{-8})^{-1/2} = \frac{1}{(16 x^{8} y^{-8})^{1/2}} = \frac{1}{4} x^{-4} y^{4} = \frac{y^{4}}{4 x^{4}}. \] So the final answer for (c) is \( \frac{y^{4}}{4 x^{4}} \).