∣−8∣−2−1+20150−2×24÷22|-8|-2^{-1}+2015^{0}-2×2^{4}÷2^{2}.

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Worked solution

1. 计算绝对值、负整数指数幂及零次幂

根据绝对值的定义、负整数指数幂性质以及零次幂的性质可得:
∣−8∣=8|-8| = 8
2−1=122^{-1} = \frac{1}{2}
20150=12015^{0} = 1

2. 计算乘除与幂的混合运算项

根据同底数幂的乘除运算法则计算最后一项:
2×24÷22=21+4−2=23=82 \times 2^{4} \div 2^{2} = 2^{1+4-2} = 2^{3} = 8

3. 代入原式进行实数四则混合运算,得出最终结果

将上述各部分简化结果代入原式,合并常数项:
原式=8−12+1−8原式 = 8 - \frac{1}{2} + 1 - 8
=(8−8)+1−12= (8 - 8) + 1 - \frac{1}{2}
=12= \frac{1}{2}

Answer

12\frac{1}{2}

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