Solve {(e)^frac{-1.99*10^-19{1.38*10^-23*300}}}

$${(e)^{ \frac{ -1.99 \times { 10 }^{ -19 } }{ 1.38 \times { 10 }^{ -23 } \times 300 } }}$$

Evaluate

$$\frac{1}{e^{\frac{9950}{207}}}\approx 1.331963411 \cdot 10^{-21}$$

Solution Steps

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

$$e^{\frac{-1.99\times 10^{4}}{1.38\times 300}}$$

Calculate 10 to the power of 4 and get 10000.

$$e^{\frac{-1.99\times 10000}{1.38\times 300}}$$

Multiply -1.99 and 10000 to get -19900.

$$e^{\frac{-19900}{1.38\times 300}}$$

Multiply 1.38 and 300 to get 414.

$$e^{\frac{-19900}{414}}$$

Reduce the fraction \frac{-19900}{414} to lowest terms by extracting and canceling out 2.

$$e^{-\frac{9950}{207}}$$