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.(1 point)
(143⋅27−7)034=

Answer 1

To simplify the expression \((14^3 \cdot 27^{-7})^{0/3^4}\), we can start by applying the properties of exponents and simplification.

1. Exponent of Zero: Any non-zero number raised to the zero power is equal to 1. \[ (14^3 \cdot 27^{-7})^{0} = 1 \]

Since anything raised to the power of zero is 1, we can evaluate the original expression as:

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

2. Denominator Calculation: The next part involves \(3^4\), but since \(1\) divided by any number is simply the number: \[ \frac{1}{3^4} = \frac{1}{81} \]

In conclusion, the final simplified expression is: \[ \frac{1}{81} \]

Thus, the answer to \((14^3 \cdot 27^{-7})^{0/3^4}\) is: \[ \boxed{\frac{1}{81}} \]