化简 [(2^4)^2]^{-3}*(2^2)^{(2^2)^2}

解答

化简

[(2^{4})^{2}]^{- 3} \cdot (2^{2})^{(2^{2})^{2}}

256

求解步骤

[(2^{4})^{2}]^{- 3} (2^{2})^{(2^{2})^{2}}

(2^{4})^{2} : 2^{8}

= [2^{8}]^{- 3} (2^{2})^{(2^{2})^{2}}

(2^{2})^{(2^{2})^{2}} : 2^{32}

= [2^{8}]^{- 3} \cdot 2^{32}

(2^{8})^{- 3} = \frac{1}{2 ^{24}}

= 2^{32} \cdot \frac{1}{2 ^{24}}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2 ^{32}}{2 ^{24}}

乘以:

1 \cdot 2^{32} = 2^{32}

= \frac{2 ^{32}}{2 ^{24}}

使用指数法则:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{2 ^{32}}{2 ^{24}} = 2^{32 - 24}

= 2^{32 - 24}

数字相减:

32 - 24 = 8

= 2^{8}

2^{8} = 256

= 256

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