Apply the Properties of Integer Exponents to generate equivalent expressions to (14^3⋅27^−7)^0/3^4

Question

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 \((14^3 \cdot 27^{-7})^{0/3^4}\), we start by simplifying \(0/3^4\).

Since \(0/3^4 = 0\), we can use the property of exponents that says any number (except zero) raised to the power of 0 is equal to 1. Consequently, we have:

\[ (14^3 \cdot 27^{-7})^{0/3^4} = (14^3 \cdot 27^{-7})^0 = 1 \]

Now, \(1\) can be expressed as a simplified fraction with no remaining exponents:

\[ 1 = \frac{1}{1} \]

Thus, the final answer is:

\[ \boxed{1} \]