Write \( A=-2 \sqrt{27}+4 \sqrt{12}-\sqrt{3^{3}} \) in the formof a \( \sqrt{b} \) where \( a \) and \( b \) are natural numbers:

Let's simplify \( A = -2 \sqrt{27} + 4 \sqrt{12} - \sqrt{3^{3}} \). First, we simplify each term: 1. \( \sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3} \), so \( -2 \sqrt{27} = -2 \times 3\sqrt{3} = -6\sqrt{3} \). 2. \( \sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3} \), so \( 4 \sqrt{12} = 4 \times 2\sqrt{3} = 8\sqrt{3} \). 3. \( \sqrt{3^3} = \sqrt{27} = 3\sqrt{3} \). Now we can substitute these back into \( A \): \[ A = -6\sqrt{3} + 8\sqrt{3} - 3\sqrt{3} \] Combine the terms: \[ A = (-6 + 8 - 3)\sqrt{3} = -1\sqrt{3} = -\sqrt{3} \] Thus, the expression is in the form \( A = -\sqrt{3} \). However, rewriting it in the format of \( a \sqrt{b} \) with positive \( a \) and \( b \): We can express it as \( A = -1\sqrt{3} \) or \( A = \sqrt{3} \) (with \( a = 1 \) and \( b = 3 \) in the proper context). So, the final answer is \( A = -\sqrt{3} \), where \( a = 1 \) and \( b = 3 \).