4.55. smplify each expression. b. \( \left(\frac{2}{3}\right)^{3} \) c. \( (2+3)^{8} \) a. \( 2\left(-\frac{1}{2}+\frac{1}{4}\right) \)

Let's break it down step by step! For \( a = 2\left(-\frac{1}{2}+\frac{1}{4}\right) \): First, simplify inside the parentheses: \(-\frac{1}{2} + \frac{1}{4} = -\frac{2}{4} + \frac{1}{4} = -\frac{1}{4}\). Now, multiply: \(2 \times -\frac{1}{4} = -\frac{1}{2}\). Now, for \( b = \left(\frac{2}{3}\right)^{3} \): This means \(\frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} = \frac{2^3}{3^3} = \frac{8}{27}\). Finally, for \( c = (2+3)^{8} \): First, add \(2 + 3 = 5\), so it becomes \(5^8\). That’s \(390625\)! (A huge number, right?) So the simplified expressions are: a. \(-\frac{1}{2}\) b. \(\frac{8}{27}\) c. \(390625\)