Solve 1/2(6.67*10^-11)(5.98*10^24*6.42*10^23)/2.64*10^3

$$\frac { 1 } { 2 } ( 6.67 \times 10 ^ { - 11 } ) \frac { ( 5.98 \times 10 ^ { 24 } \cdot 6.42 \times 10 ^ { 23 } ) } { 2.64 \times 10 ^ { 3 } }$$

Evaluate

$$\frac{533483275000000000000000000000000000}{11}\approx 4.849847955 \cdot 10^{34}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 24 and 23 to get 47.

$$\frac{1}{2}\times 6.67\times 10^{-11}\times \frac{5.98\times 10^{47}\times 6.42}{2.64\times 10^{3}}$$

Multiply \frac{1}{2} and 6.67 to get \frac{667}{200}.

$$\frac{667}{200}\times 10^{-11}\times \frac{5.98\times 10^{47}\times 6.42}{2.64\times 10^{3}}$$

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

$$\frac{667}{200}\times \frac{1}{100000000000}\times \frac{5.98\times 10^{47}\times 6.42}{2.64\times 10^{3}}$$

Multiply \frac{667}{200} and \frac{1}{100000000000} to get \frac{667}{20000000000000}.

$$\frac{667}{20000000000000}\times \frac{5.98\times 10^{47}\times 6.42}{2.64\times 10^{3}}$$

Cancel out 10^{3} in both numerator and denominator.

$$\frac{667}{20000000000000}\times \frac{5.98\times 6.42\times 10^{44}}{2.64}$$

Multiply 5.98 and 6.42 to get 38.3916.

$$\frac{667}{20000000000000}\times \frac{38.3916\times 10^{44}}{2.64}$$

Calculate 10 to the power of 44 and get 100000000000000000000000000000000000000000000.

$$\frac{667}{20000000000000}\times \frac{38.3916\times 100000000000000000000000000000000000000000000}{2.64}$$

Multiply 38.3916 and 100000000000000000000000000000000000000000000 to get 3839160000000000000000000000000000000000000000.

$$\frac{667}{20000000000000}\times \frac{3839160000000000000000000000000000000000000000}{2.64}$$

Expand \frac{3839160000000000000000000000000000000000000000}{2.64} by multiplying both numerator and the denominator by 100.

$$\frac{667}{20000000000000}\times \frac{383916000000000000000000000000000000000000000000}{264}$$

Reduce the fraction \frac{383916000000000000000000000000000000000000000000}{264} to lowest terms by extracting and canceling out 24.

$$\frac{667}{20000000000000}\times \frac{15996500000000000000000000000000000000000000000}{11}$$

Multiply \frac{667}{20000000000000} and \frac{15996500000000000000000000000000000000000000000}{11} to get \frac{533483275000000000000000000000000000}{11}.

$$\frac{533483275000000000000000000000000000}{11}$$

Factor

$$\frac{13 \cdot 29 \cdot 107 \cdot 2 ^ {27} \cdot 5 ^ {29} \cdot 23 ^ {2}}{11} = 4.849847954545454 \times 10^{34}\frac{7}{11} = 4.849847954545454 \times 10^{34}$$