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

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

Evaluate

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

Solution Steps

To multiply powers of the same base, add their exponents. Add 27 and 23 to get 50.

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

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

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

Calculate 10 to the power of -11 and get \frac{1}{100000000000}.

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

Multiply 6.67 and \frac{1}{100000000000} to get \frac{667}{10000000000000}.

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

Cancel out 10^{12} in both numerator and denominator.

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

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

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

Calculate 10 to the power of 38 and get 100000000000000000000000000000000000000.

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

Multiply 1.08 and 100000000000000000000000000000000000000 to get 108000000000000000000000000000000000000.

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

To multiply powers of the same base, add their exponents. Add 1 and 0 to get 1.

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

Calculate 1.9 to the power of 1 and get 1.9.

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

Expand \frac{108000000000000000000000000000000000000}{1.9} by multiplying both numerator and the denominator by 10.

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

Multiply \frac{667}{10000000000000} and \frac{1080000000000000000000000000000000000000}{19} to get \frac{72036000000000000000000000000}{19}.

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

Factor

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