please help

Question

 Evaluate f(x) = 8(2)^x for x = -3

Answer 1

f(x) = 8 * 2^x

 

x = -3

 

f(x) = 8 * 2^-3 = 8/2³ = 8/8 = 1

Answer 2

Lucy, a negative exponent means you move the base from the numerator to the denominator, or vice versa, and change the exponent to a positive.

 

f(-3) = 8(2)^-3 = 8/2³ = 8/8 = 1

 

Let's say it was f(x) = 8/2^-x and it asked to solve for x = -3. Then f(-3) = 8/2^-3 = 8(2)³ = 8(8) = 64.

 

You can even have it both in the numerator and denominator! 2^-3/3^-2 = 3²/2³ = 9/4, for example.

 

Hope this helps!

 

 

Answer 3

Just so you know:  In a rational expression, moving a term which has

an exponent from the numerator to the denominator or vice versa 

will change the sign on the exponent from positive to negative or the 

other way around.   Here are some examples:

 

3 / X^-5    =  3(X⁵)            ;         Y⁹   =  1 / Y^-9

                                

 

 

A^-7B⁴ / (C⁷D^-6) =  (B⁴D⁶) / (C⁷A⁷)

 

 

So in your problem:

 

       f(x) = 8(2^x)

 

     f(-3) = 8(2^-3)

 

            = 8(1/2³)

 

            = 8 (1/8)

 

            = 1