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

Transcript text: Evaluate the following expressions. \[ \begin{array}{l} (-2)^{8}=\square \\ -2^{8}=\square \end{array} \] Check Answer

Solution

Solution Steps

Step 1: Evaluate \((-2)^{8}\)

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, \((-2)^{8} = 256\).

Step 2: Evaluate \(-2^{8}\)

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

\[ \boxed{(-2)^{8} = 256, \quad -2^{8} = -256} \]

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