Apply the Properties of Integer Exponents to generate equivalent expressions to (14 raised to the 3 power⋅27 raised to the −7 power) raised to the 0 power/3 raised to the 4 power with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)

Answer 1

To solve the expression \((14^3 \cdot 27^{-7})^0 / 3^4\) using the properties of integer exponents, we will simplify it step by step.

1. Evaluate \((14^3 \cdot 27^{-7})^0\):

   • Any expression raised to the power of 0 is 1. Therefore: \[ (14^3 \cdot 27^{-7})^0 = 1 \]

2. Rewrite the expression:

   • Now, we substitute this back into the original expression: \[ \frac{1}{3^4} \]

3. Calculate \(3^4\):

   • We find \(3^4\): \[ 3^4 = 81 \]

4. Construct the final expression:

   • Therefore, the expression simplifies to: \[ \frac{1}{81} \]

Finally, the simplified answer is: \[ \boxed{\frac{1}{81}} \]