Final answer:
To calculate an exponential function from two points, you need the coordinates to derive the equation. The question provided, however, does not offer points but lists various exponential expressions with different treatments, such as squaring, multiplication, and taking roots, which involve specific mathematical manipulations.
Step-by-step explanation:
Calculating Exponential Functions:
To calculate the exponential function from two points, you would need to know the coordinates of these points and use them to determine the specific equation. However, the question seems to be mixed up and doesn't provide actual points or a clear task. Instead, it mentions different exponential expressions, which might apply to separate problems. Squaring of exponentials involves squaring the number and multiplying the exponent by two.
For example, if you have
, the squared form would be
.
In the case of multiplying powers of ten, such as
, you add the exponents to get
.
Taking square roots of exponentials requires that you take the square root of the base number and halve the exponent. For addition and subtraction of exponentials, ensure all terms are expressed with the same power of ten then add or subtract the coefficients, adjusting if necessary. If we could represent these relationships with base e (Euler's number) we could transform any power relationship into an exponential function. For instance 'b' to the power of 'x' can be represented as 'e' to the power of x ln(b) consistent with the properties of logarithms and exponentials. This is useful for higher-level manipulations of exponential functions.