Solve the equation 1/1024=4*16^2x?

We'll have to solve an exponential
equation.

We notice that the denominator of the fraction
from the left side could be written as:

1024 = 256*4 =
4*16^2

We'll multiply both sides by
4:

1/16^2 = 4*4*16^2x

1/16^2 =
16*16^2x

We'll re-write the right side using the property
of exponentials:

a^b*a^c =
a^(b+c)

16*16^2x =
16^(1+2x)

We'll re-write the
equation:

1/16^2 =
16^(1+2x)

16^(-2) =
16^(1+2x)

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

2x+1=-2

2x=-2-1

2x=-3

The
solution of the exponential equation 1/1024=4*16^2x is
x=-3/2.