Why (1/8)^0 Always Equals One: Understanding Exponential Rules

To solve the problem, $(\frac{1}{8})^0$, we utilize the Zero Exponent Rule, which states that any non-zero number raised to the power of zero equals $1$.

Here's a step-by-step explanation:

• Step 1: Identify the base and ensure it is non-zero. In this case, the base is $\frac{1}{8}$, which is indeed non-zero.
• Step 2: Apply the Zero Exponent Rule. According to this rule, $\left(\frac{1}{8}\right)^0 = 1$.
• Step 3: Conclude the result: The expression evaluates to $1$.

Therefore, the correct answer to the problem $(\frac{1}{8})^0$ is $1$.