Herrera West
05/07/2023 · High School

Apply the Properties of Integer Exponents to generate equivalent expressions to \( \frac{\left(14^{3} \cdot 27^{-7}\right)^{0}}{3^{4}} \) with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents. (1 point) \( \frac{\left(14^{3} \cdot 27^{-7}\right)^{0}}{3^{4}}=\square \) Check answer Remaining Attempts : 3

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To simplify the expression \( \frac{\left(14^{3} \cdot 27^{-7}\right)^{0}}{3^{4}} \), we can start by applying the property of exponents that states any non-zero number raised to the power of 0 is equal to 1. 1. **Evaluate the numerator**: \[ \left(14^{3} \cdot 27^{-7}\right)^{0} = 1 \] 2. **Substitute back into the expression**: \[ \frac{1}{3^{4}} \] 3. **Calculate \(3^{4}\)**: \[ 3^{4} = 81 \] 4. **Now substitute this value back into the expression**: \[ \frac{1}{81} \] Thus, the simplified expression is: \[ \frac{\left(14^{3} \cdot 27^{-7}\right)^{0}}{3^{4}} = \frac{1}{81} \] So the final answer is: \[ \frac{1}{81} \]

Quick Answer

\(\frac{1}{81}\)
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