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)
(143⋅27−7)034=

Answer 1

To simplify the expression \((14^3 \cdot 27^{-7})^0 / 34\) using the properties of integer exponents, we follow these steps:

1. Understand the Power of Zero: According to the property of exponents, any non-zero base raised to the power of zero is equal to 1. Thus, \((14^3 \cdot 27^{-7})^0 = 1\).

2. Set Up the Expression: The expression simplifies to: \[ \frac{1}{34} \]

3. Final Simplification: Since \(34\) is already a positive integer, we can express the final answer as a fraction: \[ \frac{1}{34} \]

Therefore, the final answer is: \[ \frac{1}{34} \]