exponential function #2

Question

evaluate the exponential function at the specified value of x

 

f(x)=4^x,  x= -4

Answer 1

Hey Carlos

You need to think about the rules for exponents. Is there any that tells you how to deal with negative exponents?

Here is a way to think about it.  For positive exponents you could write x^n = x*x^(n-1), as long as n is greater than 0.  This can be rewritten as: x^(n-1) = (x^n)/x, as long as x is not 0.  Now suppose n is 0, and the rule gives us: x^(-1) = x^(0)/x.  Since x^0 is 1, this means x^(-1) = 1/x.  If we assume this holds as long as n is an integer(positive or negative) and x is not 0, then we have that x^(-2) = x^(-1)/x = ([x^0]/x)/x =(1/x)/x = 1/x^2, and in general x^(-n) = 1/(x^n).  Then in your case, 4^(-4) = 1/(4^4).

From here just multiply to find: 1/(4*4*4*4)=?

 

 

Hope this is helpful,

Jose 

Answer 2

f(x) = 4^x

 

f(x=4) = 4⁴ = 4*4*4*4 = ??