How do you simplify e^{2ln x}?

To simplify e2ln x, we can use the property of exponents and logarithms. The key property is that eln a = a. This means that if we have an exponent that is multiplied by the natural logarithm, we can effectively ‘cancel out’ the e and the ln.

In this case, we start with:

e2ln x

Since we know that ln x is simply the natural logarithm of x, we can rewrite:

e2ln x = eln(x^2)

Applying the property of exponents and logarithms mentioned earlier:

eln(x^2) = x^2

Therefore, the simplified form of e2ln x is:

x²