help me use the number 'e' as a natural base.
You have to be much more specific. This question cannot be answered, it is very general. Any number can be used as a base, including 10, commonly used in the US.
Can you walk me through this problem:
(3e^(-4x))^2
What do you want to do? You cant calculate it without knowing x. Something needs to be done.
I'm trying to simplify the problem, but I don't know where to begin
Simplify:
(3e^(-4x))^2
3^2 * e^-8x
9 /e^8x
Remember that (a^b)^j = a^kb
To simplify the expression (3e^(-4x))^2, we can start by applying the power rule, which states that when raising a power to another power, we multiply the exponents. In this case, the exponent 2 is applied to both the 3 and the e^(-4x).
So, we have (3^2)*(e^(-4x))^2. Simplifying the first part, 3^2 equals 9.
Now we need to simplify the exponent of e^(-4x). Applying the power rule again, we multiply the exponent -4x by the exponent 2. This gives us e^(-8x).
Therefore, the simplified expression is 9*(e^(-8x)).
Note that e is the mathematical constant approximately equal to 2.71828, often referred to as Euler's number or the natural base. It is commonly used in exponential functions and has various applications in mathematics and science.