(6cd^-1)^-3

Answer 1

To simplify the expression \((6cd^{-1})^{-3}\), follow these steps:

1. Apply the exponent to each factor inside the parentheses: \[ (6cd^{-1})^{-3} = 6^{-3} (c)^{-3} (d^{-1})^{-3} \]

2. Calculate each component:

   • \(6^{-3} = \frac{1}{6^3} = \frac{1}{216}\)
   • \((c)^{-3} = \frac{1}{c^3}\)
   • \((d^{-1})^{-3} = d^{1 \cdot 3} = d^3\)

3. Combine the results: \[ (6cd^{-1})^{-3} = \frac{1}{216} \cdot \frac{1}{c^3} \cdot d^3 = \frac{d^3}{216c^3} \]

So, the simplified expression is: \[ \frac{d^3}{216c^3} \]