To simplify the expression \((3f^{-2})^3\) to have only one positive exponent, we apply the power of a power property, which states that \((a^m)^n = a^{m \cdot n}\).
First, distribute the exponent 3 to both the coefficient and the variable part:
\[ (3f^{-2})^3 = 3^3 \cdot (f^{-2})^3 \]
Calculating \(3^3\):
\[ 3^3 = 27 \]
Next, apply the power of a power property to \(f^{-2}\):
\[ (f^{-2})^3 = f^{-2 \cdot 3} = f^{-6} \]
Now, combine these results:
\[ (3f^{-2})^3 = 27 \cdot f^{-6} \]
To express this with only one positive exponent, we can rewrite \(f^{-6}\) as \(\frac{1}{f^6}\):
\[ 27 \cdot f^{-6} = \frac{27}{f^6} \]
Thus, the simplified expression with only one positive exponent is:
\[ \frac{27}{f^6} \]
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