Understanding Exponential Notation: Breaking Down the Expression e^xy Step by Step

e^xy

The expression e^xy represents exponential notation, where e is the base of natural logarithm and xy is the exponent

The expression e^xy represents exponential notation, where e is the base of natural logarithm and xy is the exponent. Let’s break it down step by step.

First, let’s understand what e and natural logarithm are. The value of e is an irrational number approximately equal to 2.71828. It is an important constant in mathematics, similar to π. Natural logarithm (ln) is the inverse function of exponential function with base e. In other words, ln(e^a) = a.

Now, let’s analyze the expression e^xy. Since e is the base, the expression e^xy represents e raised to the power of xy. Here, x and y can be any real numbers.

To simplify the expression, we need to understand the properties of exponential notation. The product rule of exponents states that for any real numbers a and b, and any exponent c:

a^c * b^c = (a * b)^c

Using this rule, we can simplify e^xy as follows:

e^xy = (e^x)^y

So, e^xy can be written as (e^x)^y. This means that we first take e and raise it to the power of x, and then raise the result to the power of y.

For example, if x = 2 and y = 3, we have:

e^xy = (e^2)^3 = (approximately 7.389)^3 ≈ 403.428

So, e^xy simplifies to (e^x)^y, and its value depends on the values of x and y.

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