Final answer:
The value of x satisfying the equation can be found by recognizing the structure of the equation and setting the exponents equal. However, the additional provided equations seem irrelevant to this initial problem.
Step-by-step explanation:
To determine the value of x which satisfies the equation 16⁻²⁾⁻² = 64⁻²⁾⁻², we need to recognize that both sides of the equation have a similar structure, which suggests that they could simplify in the same way. However, given the information provided, there's no direct simplification or manipulation akin to completing the square or using a known algebraic identity that can be readily applied to solve for x. Since the powers and bases are equal, the regular approach is to set the exponents equal to each other and solve the resulting equation. As such, the provided equations seem not directly relevant to the initial question.