What is the simplified expression for 3 to the power of negative 4 multiplied by 2 to the power of 3 multiplied by 3 to the power of 2 whole over 2 to the power of 4 multiplied by 3 to the power of ne?

Answer 1

To simplify the expression (\frac{3^{-4} \cdot 2^3 \cdot 3^2}{2^4 \cdot 3^n}), first combine the powers of 3 in the numerator: (3^{-4 + 2} = 3^{-2}). The expression becomes (\frac{3^{-2} \cdot 2^3}{2^4 \cdot 3^n}). Next, simplify the powers of 2: (\frac{2^3}{2^4} = 2^{-1}). Thus, the simplified expression is (\frac{2^{-1} \cdot 3^{-2}}{3^n} = \frac{2^{-1}}{3^{n+2}}).