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 will apply the properties of integer exponents step by step.

Step 1: Analyze the expression

Starting with: \[ \frac{(14^{3} \cdot 27^{-7})^{0}}{3^{4}} \]

Step 2: Apply the Zero Exponent Rule

According to the rule of exponents, any non-zero base raised to the power of zero equals 1: \[ (14^{3} \cdot 27^{-7})^{0} = 1 \]

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

Step 3: Evaluate \(3^4\)

Now we compute \(3^{4}\): \[ 3^{4} = 3 \cdot 3 \cdot 3 \cdot 3 = 81 \]

Step 4: Substitute back into the expression

Now we substitute this back into our simplified expression: \[ \frac{1}{81} \]

Final Answer

The final answer, with no remaining exponents, is: \[ \frac{1}{81} \]