answer:
To solve the equation (1/(64 ^ 2)) ^ (- x) = sqrt(1/8), we can follow these steps:
1. Simplify the left side of the equation:
(1/(64 ^ 2)) ^ (- x) = (1/64^2) ^ (- x)
2. Simplify the denominator of the fraction:
(1/64^2) ^ (- x) = (1/4096) ^ (- x)
3. Rewrite sqrt(1/8) as (1/8)^(1/2):
(1/4096) ^ (- x) = (1/8)^(1/2)
4. Simplify (1/8)^(1/2) as the square root of 1/8:
(1/4096) ^ (- x) = √(1/8)
5. Rewrite √(1/8) as (1/8)^(1/2):
(1/4096) ^ (- x) = (1/8)^(1/2)
6. Since the bases are the same, we can equate the exponents:
-x = 1/2
7. Solve for x by multiplying both sides by -1:
x = -1/2
Therefore, the solution to the equation (1/(64 ^ 2)) ^ (- x) = sqrt(1/8) is x = -1/2.