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)

Answer 1

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

1. Handling the exponent of zero: According to the properties of exponents, any non-zero number raised to the power of zero is equal to 1. Hence, we have: \[ (14^3 \cdot 27^{-7})^0 = 1 \]

2. Rewriting the expression: Now substituting this back into our expression, we get: \[ \frac{1}{3^4} \]

3. Calculating \(3^4\): We can calculate \(3^4\): \[ 3^4 = 3 \cdot 3 \cdot 3 \cdot 3 = 81 \]

4. Final expression: Now substituting this back, our expression becomes: \[ \frac{1}{81} \]

So, the final answer, which is a simplified fraction with no remaining exponents, is: \[ \boxed{\frac{1}{81}} \]