Solve 5.78*10^-9/8.46*10^25*1.6*10^-19

$$\frac{ 5.78 \times { 10 }^{ -9 } }{ 8.46 \times { 10 }^{ 25 } \times 1.6 \times { 10 }^{ -19 } }$$

Evaluate

$$\frac{289}{676800000000000000}\approx 4.270094563 \cdot 10^{-16}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 25 and -19 to get 6.

$$\frac{5.78\times 10^{-9}}{8.46\times 10^{6}\times 1.6}$$

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

$$\frac{5.78}{1.6\times 8.46\times 10^{15}}$$

Multiply 1.6 and 8.46 to get 13.536.

$$\frac{5.78}{13.536\times 10^{15}}$$

Calculate 10 to the power of 15 and get 1000000000000000.

$$\frac{5.78}{13.536\times 1000000000000000}$$

Multiply 13.536 and 1000000000000000 to get 13536000000000000.

$$\frac{5.78}{13536000000000000}$$

Expand \frac{5.78}{13536000000000000} by multiplying both numerator and the denominator by 100.

$$\frac{578}{1353600000000000000}$$

Reduce the fraction \frac{578}{1353600000000000000} to lowest terms by extracting and canceling out 2.

$$\frac{289}{676800000000000000}$$

Factor

$$\frac{17 ^ {2}}{47 \cdot 2 ^ {18} \cdot 3 ^ {2} \cdot 5 ^ {14}} = 4.270094562647754 \times 10^{-16}$$