化简 (8s^{-3}t^{-4})^2

解答

化简

(8 s^{- 3} t^{- 4})^{2}

\frac{64}{s ^{6} t ^{8}}

求解步骤

(8 s^{- 3} t^{- 4})^{2}

使用指数法则:

(a \cdot b)^{n} = a^{n} b^{n}

(8 s^{- 3} t^{- 4})^{2} = 8^{2} (s^{- 3})^{2} (t^{- 4})^{2}

= 8^{2} (s^{- 3})^{2} (t^{- 4})^{2}

8^{2} = 64

= 64 (s^{- 3})^{2} (t^{- 4})^{2}

化简

(s^{- 3})^{2} : \frac{1}{s ^{6}}

= 64 \cdot \frac{1}{s ^{6}} (t^{- 4})^{2}

化简

(t^{- 4})^{2} : \frac{1}{t ^{8}}

= 64 \cdot \frac{1}{s ^{6}} \cdot \frac{1}{t ^{8}}

化简

64 \cdot \frac{1}{s ^{6}} \cdot \frac{1}{t ^{8}} : \frac{64}{s ^{6} t ^{8}}

= \frac{64}{s ^{6} t ^{8}}

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