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(e^x)^2 = e^(2x)
In general:
(a^b)^c = a^(bc)
If the expression you're dealing with is e^(x^2), however, then no, it can not be simplified.
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How would i simplify e cubed over cube root of e squared multiplied by e to the power of thirteen?
Cube root is the same as to the power of a third; when multiplying/dividing powers of a number add/subtract the powers; when a power is to another power, multiply the powers; as it is all e to some power: e³/(e²)^(1/3) × e^13 = e³/e^(2/3) × e^13 = e^(3 - 2/3 + 13) = e^(15 1/3) = e^(46/3) Which can also be expressed as "the cube root of (e to the power 46)" or "(the cube root of e) to the power 46".
What is x if e to the x power equals xto the 2 power?
Very close to -0.70348
What is the exact solution of e to the x power subtract 2 equals 8?
e^x - 2 = 8 e^x = 10 So x = ln(10) = 1/log10(e)
What is the derivative of e to the power ln x squared?
e^[ln(x^2)]=x^2, so your question is really, "What is the derivative of x^2," to which the answer is 2x.
How do you manually calculate i to the power of i?
i (taken to be sqrt(-1) for this question) requires that you know a bit about writing complex numbers. i = e^(i*pi/2) so i^i = (e^(i*pi/2))^i which equals e^(i*i*pi/2) since i*i = -1 we get e^(-pi/2) so i^i = e^(-pi/2) which is roughly .207879576
