Solve 6.62510^-34310^8/1.3810^23300*57010^-9

$$\frac{ 6.625 { 10 }^{ -34 } 3 { 10 }^{ 8 } }{ 1.38 { 10 }^{ 23 } 300 \cdot 570 { 10 }^{ -9 } }$$

Evaluate

$$\frac{53}{6292800000000000000000000000000000000000000000}\approx 8.422323926 \cdot 10^{-45}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -34 and 8 to get -26.

$$\frac{6.625\times 10^{-26}\times 3}{1.38\times 10^{23}\times 300\times 570\times 10^{-9}}$$

To multiply powers of the same base, add their exponents. Add 23 and -9 to get 14.

$$\frac{6.625\times 10^{-26}\times 3}{1.38\times 10^{14}\times 300\times 570}$$

Cancel out 3 in both numerator and denominator.

$$\frac{6.625\times 10^{-26}}{1.38\times 100\times 570\times 10^{14}}$$

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

$$\frac{6.625}{1.38\times 100\times 570\times 10^{40}}$$

Multiply 1.38 and 100 to get 138.

$$\frac{6.625}{138\times 570\times 10^{40}}$$

Multiply 138 and 570 to get 78660.

$$\frac{6.625}{78660\times 10^{40}}$$

Calculate 10 to the power of 40 and get 10000000000000000000000000000000000000000.

$$\frac{6.625}{78660\times 10000000000000000000000000000000000000000}$$

Multiply 78660 and 10000000000000000000000000000000000000000 to get 786600000000000000000000000000000000000000000.

$$\frac{6.625}{786600000000000000000000000000000000000000000}$$

Expand \frac{6.625}{786600000000000000000000000000000000000000000} by multiplying both numerator and the denominator by 1000.

$$\frac{6625}{786600000000000000000000000000000000000000000000}$$

Reduce the fraction \frac{6625}{786600000000000000000000000000000000000000000000} to lowest terms by extracting and canceling out 125.

$$\frac{53}{6292800000000000000000000000000000000000000000}$$

Factor

$$\frac{53}{19 \cdot 23 \cdot 2 ^ {45} \cdot 3 ^ {2} \cdot 5 ^ {41}} = 8.422323925756421 \times 10^{-45}$$