Questions: Determine the value of (3^3)^2. (A) 711 (B) 645 (C) 729 (D) 12

Solution Steps

The given expression is \((3^{3})^{2}\). We can simplify this using the power of a power property, which states that \((a^m)^n = a^{m \cdot n}\).

\[ (3^{3})^{2} = 3^{3 \cdot 2} = 3^{6} \]

Now, we need to calculate \(3^{6}\).

\[ 3^{6} = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \]

Calculating step-by-step:

\[ 3 \times 3 = 9 \] \[ 9 \times 3 = 27 \] \[ 27 \times 3 = 81 \] \[ 81 \times 3 = 243 \] \[ 243 \times 3 = 729 \]

Final Answer