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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
Solution of e to the power of -2?
e to the power -2 = 2.71828183 to power -2 = 0.135335283
What is the value of e to the power of (2x) when e to the power of x equals 2?
The power law of indices says: (x^a)^b = x^(ab) = x^(ba) = (x^b)^a → e^(2x) = (e^x)² but e^x = 2 → e^(2x) = (e^x)² = 2² = 4
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 the value of e to the -2 power?
e-2 = 1/e2 ≈ 0.1353
What is the second derivative of xsqaured e to the power of x?
f(x) = (x^2)(e^x)f'(x) = e^x((x^2)+2x) - i thinkf"(x) = ?--------f(x) = (x^2)(e^x)apply the power rulef'(x) = (x^2)(e^x) + (2x)(e^x)apply the power rule to the first part and apply the power rule to the second part, then add those togetherf''(x) = [(x^2)(e^x) + (2x)(e^x)] + [(2x)(e^x) + (2)(e^x)]simplifyf''(x) = (e^x)(x^2 + 4x +2)I got it right. It checked out on my calculator.
Solve e to the power ln2?
ln is the inverse of e. So the e and the ln cancel each other out and you are left with 2. eln2 = 2
How can you make rational of i power i?
It is NOT rational, but it IS real.Start with Euler's formula: e^ix = cos(x) + i*sin(x) for all x.When x = pi/2,e^(i*pi/2) = cos(pi/2) + i*sin(pi/2) = 0 + i*1 = ior i = e^(i*pi/2)Raising both sides to the power i givesi^i = e^[i*(i*pi/2)] = e^[i*i*pi/2]and since i*i = -1,i^i = e^(-pi/2) = 0.20788, approx.
What is the derivative of e to the power of -2 times x?
e^(-2x) * -2 The derivative of e^F(x) is e^F(x) times the derivative of F(x)
What are the release dates for Horsepower TV - 2006 E-rod Powered Supercar?
Horsepower TV - 2006 E-rod Powered Supercar was released on: USA: April 2010
What is the derivative of x to the power of e?
e^[ln(x^2)]=x^2, so your question is really, "What is the derivative of x^2," to which the answer is 2x.
What is x if e to the x power equals xto the 2 power?
Very close to -0.70348
How do you integrate e power minus 2x?
∫e^(-2x) dx Let u = 2x du= 2 dx dx=(1/2) du ∫e^(-2x) dx = (1/2) ∫e^-u du = (1/2) (-e^-u) = -e^-u /2 + C = -e^-(2x) / 2 + C
