Apply the Properties of Integer Exponents to generate equivalent expressions to (14^3⋅27^−7)^0/34

Question

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 \((14^3 \cdot 27^{-7})^0/34\), we start by applying the properties of exponents.

1. Property of Exponent: Any non-zero base raised to the power of zero equals 1. Thus, the expression \((14^3 \cdot 27^{-7})^0\) simplifies to \(1\).

   \[ (14^3 \cdot 27^{-7})^0 = 1 \]

2. Substituting back into the expression: The original expression now simplifies to:

   \[ \frac{1}{34} \]

3. Since \(34\) is already a positive integer, we do not need to convert or simplify further with respect to exponents. There are no remaining exponents in this fraction.

Therefore, the simplified expression is:

\[ \frac{1}{34} \]

Thus, the answer is \(\boxed{\frac{1}{34}}\).