4x^4-(5x^4) -4x^5+5x^5 27x^3((1)/(3)x) 3(-2x^3)^2

Let's go through each expression step by step:<br /><br />1. \(4x^{4} - (5x^{4})\)<br /><br /> Simplify the expression:<br /> \[<br /> 4x^{4} - 5x^{4} = (4 - 5)x^{4} = -x^{4}<br /> \]<br /><br />2. \(-4x^{5} + 5x^{5}\)<br /><br /> Simplify the expression:<br /> \[<br /> -4x^{5} + 5x^{5} = (-4 + 5)x^{5} = x^{5}<br /> \]<br /><br />3. \(27x^{3}(\frac{1}{3}x)\)<br /><br /> Simplify the expression:<br /> \[<br /> 27x^{3} \cdot \frac{1}{3}x = 27 \cdot \frac{1}{3} \cdot x^{3} \cdot x = 9x^{4}<br /> \]<br /><br />4. \(3(-2x^{3})^{2}\)<br /><br /> Simplify the expression:<br /> \[<br /> 3(-2x^{3})^{2} = 3 \cdot (-2)^{2} \cdot (x^{3})^{2} = 3 \cdot 4 \cdot x^{6} = 12x^{6}<br /> \]<br /><br />So, the simplified forms of the given expressions are:<br />1. \(-x^{4}\)<br />2. \(x^{5}\)<br />3. \(9x^{4}\)<br />4. \(12x^{6}\)