you select values of x and then you use the equation to find values of y.
then you plot them on the graph.
i chose x = -3,-2,-1,0,1,2,3
it was enough to show the general shape of the graph.
two examples of use of the formula are shown below:
when x = -2:
y = (1/5)^(x-1) becomes:
y = 1^(x-1) / (5^(x-1) which becomes:
y = 1 / 5^(-2-1) whicy becomes:
y = 1 / 5^(-3) which becomes:
y = 1 / (1/5^3) which becomes:
y = 1 * 5^3/1 which becomes:
y = 1 * 5^3 which becomes:
y = 1 * 125 which becomes:
y = 125
when x = -2, y = 125 as shown on the graph.
when x = 2 it's a little simpler because you're not dealing with negative exponents.
when x = 2:
y = (1/5)^(x-1) becomes:
y = (1/5)^(2-1) which becomes:
y = (1/5)^1 which becomes:
y = 1/5 which is the same as y = .2 as shown on the graph.
the basic concepts used are:
a^-2 = 1/a^x
this first one means that any value raised to a negative exponent is the same as the reciprocal of that value taised to a positive exponent.
1/(a/b) = 1 * (b/a)
this second one means that, when you divide by a fraction, it's the same thing as multiplying by the reciprocal of the fraction.
some links you might find useful.
http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut29_negexp.htm
http://www.purplemath.com/modules/fraction3.htm