Lutasin ang 6.67*10^-111.90*10^27*(1.08*10^23)/(1.9*10^6)*(1.9*{10^6)}

$$6.67 \times { 10 }^{ -11 } \frac{ 1.90 \times { 10 }^{ 27 } \times (1.08 \times { 10 }^{ 23 } ) }{ (1.9 \times { 10 }^{ 6 } ) \times (1.9 \times { 10 }^{ 6 } ) }$$

I-evaluate

$$\frac{72036000000000000000000000000}{19}\approx 3.791368421 \cdot 10^{27}$$

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 27 at 23 para makuha ang 50.

$$6.67\times 10^{-11}\times \frac{1.9\times 10^{50}\times 1.08}{1.9\times 10^{6}\times 1.9\times 10^{6}}$$

Para mag-multiply ng mga power na may parehong base, i-add ang mga exponent ng mga ito. I-add ang 6 at 6 para makuha ang 12.

$$6.67\times 10^{-11}\times \frac{1.9\times 10^{50}\times 1.08}{1.9\times 10^{12}\times 1.9}$$

Kalkulahin ang 10 sa power ng -11 at kunin ang \frac{1}{100000000000}.

$$6.67\times \frac{1}{100000000000}\times \frac{1.9\times 10^{50}\times 1.08}{1.9\times 10^{12}\times 1.9}$$

I-multiply ang 6.67 at \frac{1}{100000000000} para makuha ang \frac{667}{10000000000000}.

$$\frac{667}{10000000000000}\times \frac{1.9\times 10^{50}\times 1.08}{1.9\times 10^{12}\times 1.9}$$

I-cancel out ang 10^{12} sa parehong numerator at denominator.

$$\frac{667}{10000000000000}\times \frac{1.08\times 1.9\times 10^{38}}{1.9\times 1.9}$$

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

$$\frac{667}{10000000000000}\times \frac{1.08\times 10^{38}}{1.9\times 1.9^{0}}$$

Kalkulahin ang 10 sa power ng 38 at kunin ang 100000000000000000000000000000000000000.

$$\frac{667}{10000000000000}\times \frac{1.08\times 100000000000000000000000000000000000000}{1.9\times 1.9^{0}}$$

I-multiply ang 1.08 at 100000000000000000000000000000000000000 para makuha ang 108000000000000000000000000000000000000.

$$\frac{667}{10000000000000}\times \frac{108000000000000000000000000000000000000}{1.9\times 1.9^{0}}$$

Para mag-multiply ng mga power na may parehong base, i-add ang mga exponent ng mga ito. I-add ang 1 at 0 para makuha ang 1.

$$\frac{667}{10000000000000}\times \frac{108000000000000000000000000000000000000}{1.9^{1}}$$

Kalkulahin ang 1.9 sa power ng 1 at kunin ang 1.9.

$$\frac{667}{10000000000000}\times \frac{108000000000000000000000000000000000000}{1.9}$$

I-expand ang \frac{108000000000000000000000000000000000000}{1.9} sa pamamagitan ng pag-multiply sa parehong numerator at denominator ng 10.

$$\frac{667}{10000000000000}\times \frac{1080000000000000000000000000000000000000}{19}$$

I-multiply ang \frac{667}{10000000000000} at \frac{1080000000000000000000000000000000000000}{19} para makuha ang \frac{72036000000000000000000000000}{19}.

$$\frac{72036000000000000000000000000}{19}$$

I-factor

$$\frac{23 \cdot 29 \cdot 2 ^ {26} \cdot 3 ^ {3} \cdot 5 ^ {24}}{19} = 3.7913684210526317 \times 10^{27}\frac{9}{19} = 3.7913684210526317 \times 10^{27}$$