Simplify the Fraction Expression: 8/8⁴ Step-by-Step

To solve the expression $\frac{8}{8^4}$, we will simplify it using the exponent rule for dividing powers with the same base:

• Step 1: Identify the expression as $\frac{8^1}{8^4}$. Both terms have base 8.
• Step 2: Apply the formula $\frac{a^m}{a^n} = a^{m-n}$. Here, $m = 1$ and $n = 4$.
• Step 3: Perform the subtraction in the exponent: $8^{1-4}$.

Now, calculating the exponent:

$8^{1-4} = 8^{-3}$.

We know that a negative exponent indicates the reciprocal, so:

$8^{-3} = \frac{1}{8^3}$.

Thus, the simplified expression is $\frac{1}{8^3}$.

Based on the choices given, the correct option is:

• $\frac{1}{8^3}$ (Choice 1): This matches our simplified expression.
• $8^3$ (Choice 2): Incorrect, as it does not simplify the division.
• $8^{-4}$ (Choice 3): Incorrect, because it incorrectly represents the situation.
• $8^4$ (Choice 4): Incorrect, as it doesn't simplify the expression.

Therefore, the solution to the problem is: $\frac{1}{8^3}$.

I am confident in the correctness of this solution.