Questions: Evaluate the following expressions. (-2)^8= -2^8=

Solution Steps

The expression $(-2)^{8}$ means that $-2$ is raised to the 8th power. Since the exponent is even, the result will be positive. We calculate: $$(-2)^{8} = (-2) \times (-2) \times (-2) \times (-2) \times (-2) \times (-2) \times (-2) \times (-2).$$ Simplifying step by step: $$(-2)^{2} = 4, \quad (-2)^{4} = 16, \quad (-2)^{6} = 64, \quad (-2)^{8} = 256.$$ Thus, $(-2)^{8} = 256$.

The expression $-2^{8}$ means that $2$ is raised to the 8th power first, and then the negative sign is applied. We calculate: $$2^{8} = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 256.$$ Then, apply the negative sign: $$-2^{8} = -256.$$

Final Answer