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

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
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Solution

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Solution Steps

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

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


Step 2: Evaluate 28-2^{8}

The expression 28-2^{8} means that 22 is raised to the 8th power first, and then the negative sign is applied. We calculate: 28=2×2×2×2×2×2×2×2=256. 2^{8} = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 256. Then, apply the negative sign: 28=256. -2^{8} = -256.


Final Answer

(2)8=256,28=256 \boxed{(-2)^{8} = 256, \quad -2^{8} = -256}

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