Question

Simplify the expression to have only one positive exponent.

(3f−2)3

Answer 1

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:

\[
\frac{27}{f^6}
\]