Apply the Properties of Integer Exponents to generate equivalent expressions to (14^3⋅27−7)^0 / 3^4 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.

Answer 1

To simplify the expression \((14^3 \cdot 27^{-7})^0 / 3^4\), we start by applying the properties of integer exponents.

1. Property of Exponents: Any non-zero number raised to the power of 0 is 1. Therefore: \[ (14^3 \cdot 27^{-7})^0 = 1 \]

2. Now, substitute this back into the expression: \[ \frac{1}{3^4} \]

3. Next, we simplify \(3^4\): \[ 3^4 = 81 \] Thus, the expression becomes: \[ \frac{1}{81} \]

Since we need the final answer to be a simplified fraction with no remaining exponents, we have: \[ \text{Final Answer: } \frac{1}{81} \]