Given the equation:\

1/8 = 16^x

First we will simplify 8 and 16 as powers of the prime number 2.

We know that:

8 = 2*2*2 = 2^3

16 = 4*4 = 2*2*2*2 = 2^4

Now we will rewrite into the given equation:

==> 1/(2^3) = (2^4)^x

Now we will use the exponent properties to solve.

We know that:

1/a^x = a^-x Therefore, 1/2^3 = 2^-3

Also, we know that:

(x^a)^b = x^(ab). Therefore, 2^4^x = 2^(4x)

Now we will substitute into the equation.

==> 2^-3 = 2^4x

Now since the bases are equal, then the powers are equal too.

==> -3 = 4x

We will divide by 4 to solve for x.

**==> x = -3/4**

To solve for x: 1/8 = 16^x.

LHS = 1/8 = 1/2^# = 1/2^(-3).

RHS = 16^x = (2^4)^x = 2^4x.

Therefore the given equation is rewritten as:

2^(-3) = 2^4x.

Or 2^4x = 2^(-3).

The bases are same. So we equate the exponents:

4x = -3.

4x/4 = -3/4

**x = -0.75**

** **

The equation 1/8=16^x has to be solved for x.

8 can be written as a power of 2, `8 = 2^3` . Similarly, `16 = 2^4` . The given equation can be written as:

`1/2^3 = (2^4)^x`

Use the relation `a^-1 = 1/a` , `(a^b)^c = (a^c)^b`

`2^-3 = (2^x)^4`

`2^(-3/4) = 2^x`

As the base is the same the exponent can be equated to solve for x.

x = -3/4

The solution of the equation is x = -3/4