Question: Simplify and write as a single power. \[ \frac{3^2 \times 3^1}{3^2} \] Options: -…

Simplify and write as a single power.

\[ \frac{3^2 \times 3^1}{3^2} \]

Options:

• \(3^{\frac{1}{2}}\)
• \(3^2\)
• \(3^{13}\)
• \(3^6\)

Solution

To simplify and write the expression as a single power, follow these steps: Given expression: \[ \frac{3^2 \cdot 3^3}{3^8} \] Use the rule that \(a^m \cdot a^n = a^{m+n}\) to simplify the numerator: \[ 3^2 \cdot 3^3 = 3^{2+3} = 3^5 \] Now we have: \[ \frac{3^5}{3^8} \] Use the rule that \(\frac{a^m}{a^n} = a^{m-n}\): \[ 3^{5-8} = 3^{-3} \] The expression simplifies to: \[ 3^{-3} \] \[ \text{None of the given options match } 3^{-3}. \] Re-evaluate if there’s a mistake, or the correct option might involve recognizing properties of the number.