Lutasin ang frac{(-27)^{3}(32)^{-5}(-8)^{5}(25^{2})^-6}{(-72)^4(-50^3)^4}

$$\frac { ( - 27 ) ^ { 3 } ( 32 ) ^ { - 5 } ( - 8 ) ^ { 5 } ( 25 ^ { 2 } ) ^ { - 6 } } { ( - 72 ) ^ { 4 } ( - 50 ^ { 3 } ) ^ { 4 } }$$

I-evaluate

$$\frac{3}{61035156250000000000000000000000000000000000}=4.9152 \cdot 10^{-44}$$

Mga Hakbang ng Solution

Para mag-raise ng power ng numero gamit ang ibang power, i-multiply ang mga exponent. I-multiply ang 2 at -6 para makuha ang -12.

$$\frac{\left(-27\right)^{3}\times 32^{-5}\left(-8\right)^{5}\times 25^{-12}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Kalkulahin ang -27 sa power ng 3 at kunin ang -19683.

$$\frac{-19683\times 32^{-5}\left(-8\right)^{5}\times 25^{-12}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Kalkulahin ang 32 sa power ng -5 at kunin ang \frac{1}{33554432}.

$$\frac{-19683\times \frac{1}{33554432}\left(-8\right)^{5}\times 25^{-12}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

I-multiply ang -19683 at \frac{1}{33554432} para makuha ang -\frac{19683}{33554432}.

$$\frac{-\frac{19683}{33554432}\left(-8\right)^{5}\times 25^{-12}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Kalkulahin ang -8 sa power ng 5 at kunin ang -32768.

$$\frac{-\frac{19683}{33554432}\left(-32768\right)\times 25^{-12}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

I-multiply ang -\frac{19683}{33554432} at -32768 para makuha ang \frac{19683}{1024}.

$$\frac{\frac{19683}{1024}\times 25^{-12}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Kalkulahin ang 25 sa power ng -12 at kunin ang \frac{1}{59604644775390625}.

$$\frac{\frac{19683}{1024}\times \frac{1}{59604644775390625}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

I-multiply ang \frac{19683}{1024} at \frac{1}{59604644775390625} para makuha ang \frac{19683}{61035156250000000000}.

$$\frac{\frac{19683}{61035156250000000000}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Kalkulahin ang -72 sa power ng 4 at kunin ang 26873856.

$$\frac{\frac{19683}{61035156250000000000}}{26873856\left(-50^{3}\right)^{4}}$$

Kalkulahin ang 50 sa power ng 3 at kunin ang 125000.

$$\frac{\frac{19683}{61035156250000000000}}{26873856\left(-125000\right)^{4}}$$

Kalkulahin ang -125000 sa power ng 4 at kunin ang 244140625000000000000.

$$\frac{\frac{19683}{61035156250000000000}}{26873856\times 244140625000000000000}$$

I-multiply ang 26873856 at 244140625000000000000 para makuha ang 6561000000000000000000000000.

$$\frac{\frac{19683}{61035156250000000000}}{6561000000000000000000000000}$$

Ipakita ang \frac{\frac{19683}{61035156250000000000}}{6561000000000000000000000000} bilang isang single fraction.

$$\frac{19683}{61035156250000000000\times 6561000000000000000000000000}$$

I-multiply ang 61035156250000000000 at 6561000000000000000000000000 para makuha ang 400451660156250000000000000000000000000000000000.

$$\frac{19683}{400451660156250000000000000000000000000000000000}$$

Bawasan ang fraction \frac{19683}{400451660156250000000000000000000000000000000000} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 6561.

$$\frac{3}{61035156250000000000000000000000000000000000}$$

I-factor

$$\frac{3}{2 ^ {34} \cdot 5 ^ {48}} = 4.9152000000000005 \times 10^{-44}$$