Question

Apply the properties of integer exponents to generate equivalent expressions to in parentheses we had 14 with the power of 3×27 with a power of negative -7 on the outside of the parentheses is a power of zero over three with the power of four 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 \((14^3 \times 27^{-7})^0 / 3^4\) with only positive exponents, we can follow these steps:

1. Apply the Power of Zero Rule:

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

2. Rewrite the Expression:

   • Now our expression becomes: \[ \frac{1}{3^4} \]

3. Calculate \(3^4\): \[ 3^4 = 3 \times 3 \times 3 \times 3 = 81 \]

4. Create the Simplified Expression:

   • Thus, we have: \[ \frac{1}{81} \]

This fraction \( \frac{1}{81} \) is already in its simplest form with no remaining exponents.

The final answer is: \[ \frac{1}{81} \]