Examine the Power of Inversion: Simplify 300^-4 x (1/300)^-4

To solve the problem $300^{-4} \cdot \left(\frac{1}{300}\right)^{-4}$, let's follow these steps:

• Step 1: Simplify the reciprocal power expression.
  The expression $\left(\frac{1}{300}\right)^{-4}$ can be simplified using the rule for reciprocals, which states $\left(\frac{1}{a}\right)^{-n} = a^n$. Thus, $\left(\frac{1}{300}\right)^{-4} = 300^4$.
• Step 2: Combine the powers.
  Now the expression becomes $300^{-4} \cdot 300^4$. Using the rule $a^m \cdot a^n = a^{m+n}$, we have $300^{-4+4} = 300^0$.
• Step 3: Calculate the final result.
  By the identity $a^0 = 1$, any non-zero number raised to the power of zero equals 1. Therefore, $300^0 = 1$.

Thus, the solution to the problem is $\boxed{1}$.