Solve 6.6710^-73.1510^24806/left(8.97310^3right)^2

$$\frac{ 6.67 { 10 }^{ -7 } 3.15 { 10 }^{ 24 } 806 }{ { \left(8.973 { 10 }^{ 3 } \right) }^{ 2 } }$$

Evaluate

$$\frac{188160700000000000000}{8946081}\approx 2.103275166 \cdot 10^{13}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -7 and 24 to get 17.

$$\frac{6.67\times 10^{17}\times 3.15\times 806}{\left(8.973\times 10^{3}\right)^{2}}$$

Calculate 10 to the power of 17 and get 100000000000000000.

$$\frac{6.67\times 100000000000000000\times 3.15\times 806}{\left(8.973\times 10^{3}\right)^{2}}$$

Multiply 6.67 and 100000000000000000 to get 667000000000000000.

$$\frac{667000000000000000\times 3.15\times 806}{\left(8.973\times 10^{3}\right)^{2}}$$

Multiply 667000000000000000 and 3.15 to get 2101050000000000000.

$$\frac{2101050000000000000\times 806}{\left(8.973\times 10^{3}\right)^{2}}$$

Multiply 2101050000000000000 and 806 to get 1693446300000000000000.

$$\frac{1693446300000000000000}{\left(8.973\times 10^{3}\right)^{2}}$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{1693446300000000000000}{\left(8.973\times 1000\right)^{2}}$$

Multiply 8.973 and 1000 to get 8973.

$$\frac{1693446300000000000000}{8973^{2}}$$

Calculate 8973 to the power of 2 and get 80514729.

$$\frac{1693446300000000000000}{80514729}$$

Reduce the fraction \frac{1693446300000000000000}{80514729} to lowest terms by extracting and canceling out 9.

$$\frac{188160700000000000000}{8946081}$$

Factor

$$\frac{7 \cdot 13 \cdot 23 \cdot 29 \cdot 31 \cdot 2 ^ {14} \cdot 5 ^ {14}}{3 ^ {2} \cdot 997 ^ {2}} = 21032751659637\frac{2983787}{8946081} = 21032751659637.332$$