Simplifying an exponential expression.

Question

maybe this is a stupid question but I have the following expression:

$ 10^{-18}(e^{50,9702078⋅0,75}) = 10^{-18}(4⋅10^{16}) $

How would I go about simplifying the big exponent on the left to what's on the right? With the use of a calculator.

Thanks a lot!

Answer 1

First calculate $50.9702078 \times 0.75 = 38.22765585$. Now there should be a button on your calculator called $e^x$ or something similar. Depending on your calculator, you may have to hit SHIFT $+ \ln$ to use this function.

$$e^{38.22765585} \approx 4.0000000039 \times 10^{16}.$$

Answer 2

You can't simplify it, the equality ${\rm e}^{50,9702078⋅0,75} = 4⋅10^{16}$ is valid only approximately (check it by taking the natural logarithm in both sides: $50,9702078⋅0,75 = \ln 4 + 16 \ln 10$).