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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Tutor-Verified Answer
Step-by-step Solution
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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