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