Question
Apply the Properties of Integer Exponents to generate equivalent expressions to (14 raised to the 3 power⋅27 raised to the −7 power) raised to the 0 power/3 raised to the 4 power with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
Answers
GPT-4o mini
To solve the expression \((14^3 \cdot 27^{-7})^0 / 3^4\) using the properties of integer exponents, we will simplify it step by step.
1. **Evaluate \((14^3 \cdot 27^{-7})^0\)**:
- Any expression raised to the power of 0 is 1. Therefore:
\[
(14^3 \cdot 27^{-7})^0 = 1
\]
2. **Rewrite the expression**:
- Now, we substitute this back into the original expression:
\[
\frac{1}{3^4}
\]
3. **Calculate \(3^4\)**:
- We find \(3^4\):
\[
3^4 = 81
\]
4. **Construct the final expression**:
- Therefore, the expression simplifies to:
\[
\frac{1}{81}
\]
Finally, the simplified answer is:
\[
\boxed{\frac{1}{81}}
\]
1. **Evaluate \((14^3 \cdot 27^{-7})^0\)**:
- Any expression raised to the power of 0 is 1. Therefore:
\[
(14^3 \cdot 27^{-7})^0 = 1
\]
2. **Rewrite the expression**:
- Now, we substitute this back into the original expression:
\[
\frac{1}{3^4}
\]
3. **Calculate \(3^4\)**:
- We find \(3^4\):
\[
3^4 = 81
\]
4. **Construct the final expression**:
- Therefore, the expression simplifies to:
\[
\frac{1}{81}
\]
Finally, the simplified answer is:
\[
\boxed{\frac{1}{81}}
\]