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

Question

with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
(14 to the power of 3 ⋅ 27 to the power of −7) to the power of 0 / 3 to the power of 4=

Answer 1

To apply the properties of integer exponents, let's first simplify the expression step-by-step.

1. Understanding the expression: \[ \frac{(14^3 \cdot 27^{-7})^0}{3^4} \]

2. Simplifying the power of zero: According to the property of exponents, any non-zero number raised to the power of zero is 1. Therefore: \[ (14^3 \cdot 27^{-7})^0 = 1 \]

3. Now, the expression simplifies to: \[ \frac{1}{3^4} \]

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

5. Constructing the final expression: \[ \frac{1}{3^4} = \frac{1}{81} \]

Thus, the final simplified fraction, with no remaining exponents, is:

\[ \boxed{\frac{1}{81}} \]