Question

Consider the following. f(x)=8 x²(x+4)

(a) Use a geometric series to represent the function as a power series centered at 0 . \[ f(x)=sum_{k=0}] (b) Determine the radius oF Circle

Answer 1

To simplify the expression x⁹ * x⁻⁹ using the properties of exponents, combine the bases and subtract the exponents. The final result is 1.

Step-by-step explanation:

To simplify the expression x⁹ * x⁻⁹ using the properties of exponents, we can combine the bases and subtract the exponents. Since both bases are the same (x), we subtract the exponent of x in the second term from the exponent of x in the first term. So, x⁹ * x⁻⁹ becomes x^(9-9) = x^0.

Any number raised to the power of 0 is equal to 1. Therefore, x^0 = 1.