Lutasin ang frac{9*10^{8}*(16*10^{-19})^2}{667*10^-11*91*10^-31*166*10^-27}

$$\frac { 9 \times 10 ^ { 8 } \times ( 16 \times 10 ^ { - 19 } ) ^ { 2 } } { 667 \times 10 ^ { - 11 } \times 91 \times 10 ^ { - 31 } \times 166 \times 10 ^ { - 27 } }$$

I-evaluate

$$\frac{1152000000000000000000000000000000000000000}{5037851}\approx 2.286689305 \cdot 10^{35}$$

Mga Hakbang ng Solution

Para mag-multiply ng mga power na may parehong base, i-add ang mga exponent ng mga ito. I-add ang -11 at -31 para makuha ang -42.

$$\frac{9\times 10^{8}\times \left(16\times 10^{-19}\right)^{2}}{667\times 10^{-42}\times 91\times 166\times 10^{-27}}$$

Para mag-multiply ng mga power na may parehong base, i-add ang mga exponent ng mga ito. I-add ang -42 at -27 para makuha ang -69.

$$\frac{9\times 10^{8}\times \left(16\times 10^{-19}\right)^{2}}{667\times 10^{-69}\times 91\times 166}$$

Para magi-divide ng mga power na may parehong base, i-subtract ang exponent ng denominator mula sa exponent ng numerator.

$$\frac{9\times 10^{77}\times \left(16\times 10^{-19}\right)^{2}}{91\times 166\times 667}$$

Kalkulahin ang 10 sa power ng 77 at kunin ang 100000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{9\times 100000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(16\times 10^{-19}\right)^{2}}{91\times 166\times 667}$$

I-multiply ang 9 at 100000000000000000000000000000000000000000000000000000000000000000000000000000 para makuha ang 900000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{900000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(16\times 10^{-19}\right)^{2}}{91\times 166\times 667}$$

Kalkulahin ang 10 sa power ng -19 at kunin ang \frac{1}{10000000000000000000}.

$$\frac{900000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(16\times \frac{1}{10000000000000000000}\right)^{2}}{91\times 166\times 667}$$

I-multiply ang 16 at \frac{1}{10000000000000000000} para makuha ang \frac{1}{625000000000000000}.

$$\frac{900000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(\frac{1}{625000000000000000}\right)^{2}}{91\times 166\times 667}$$

Kalkulahin ang \frac{1}{625000000000000000} sa power ng 2 at kunin ang \frac{1}{390625000000000000000000000000000000}.

$$\frac{900000000000000000000000000000000000000000000000000000000000000000000000000000\times \frac{1}{390625000000000000000000000000000000}}{91\times 166\times 667}$$

I-multiply ang 900000000000000000000000000000000000000000000000000000000000000000000000000000 at \frac{1}{390625000000000000000000000000000000} para makuha ang 2304000000000000000000000000000000000000000.

$$\frac{2304000000000000000000000000000000000000000}{91\times 166\times 667}$$

I-multiply ang 91 at 166 para makuha ang 15106.

$$\frac{2304000000000000000000000000000000000000000}{15106\times 667}$$

I-multiply ang 15106 at 667 para makuha ang 10075702.

$$\frac{2304000000000000000000000000000000000000000}{10075702}$$

Bawasan ang fraction \frac{2304000000000000000000000000000000000000000}{10075702} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 2.

$$\frac{1152000000000000000000000000000000000000000}{5037851}$$

I-factor

$$\frac{2 ^ {46} \cdot 3 ^ {2} \cdot 5 ^ {39}}{7 \cdot 13 \cdot 23 \cdot 29 \cdot 83} = 2.2866893046261194 \times 10^{35}\frac{336198}{5037851} = 2.2866893046261194 \times 10^{35}$$