Apply the Properties of Integer Exponents to generate equivalent expressions to (14^3⋅2^7−7)^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 \((14^3 \cdot 2^7 - 7)^0 / 3^4\), we can follow these steps:

1. Evaluate the exponent: The exponent \(0\) indicates that any non-zero quantity raised to the power of \(0\) equals \(1\). Therefore, we evaluate

   \[ (14^3 \cdot 2^7 - 7)^0 = 1 \]

2. Consider the full expression: After evaluating the exponent, our expression simplifies to

   \[ \frac{1}{3^4} \]

3. Calculate \(3^4\):

   \[ 3^4 = 81 \]

4. Rewrite the expression: Now, substituting back into our expression we have

   \[ \frac{1}{81} \]

Thus, the simplified expression is

\[ \frac{1}{81} \]

This fraction has no remaining exponents, and it is already in its simplest form.

The final answer is

\[ \frac{1}{81} \]