Solve the equation 1/2^(x^2-1)=square root(16^x).

We'll manipulate the left side using the negative power
property:

1/2^(x^2-1)=2^-(x^2-1)

Now,
we'll manipulate the right side, writting 16 as a power of
2:

sqrt(16^x) = sqrt(2^4x) = (2^4x)^(1/2) =
2^2x

We'll re-write the
equation:

2^-(x^2-1) =
2^2x

Since the bases are matching now, we'll apply one to
one property:

-x^2+1 = 2x

x^2
+ 2x - 1 = 0

x1 = [-2+sqrt(4 +
4)]/2

x1 = (-2+2sqrt2)/2

x1 =
-1+sqrt2

x2 =
-1-sqrt2

The solutions of exponential
equation are { -1-sqrt2 ; -1+sqrt2}.