Question

which single power is equivalent to the expression $3^{4}cdot \frac{3^{3}}{3^{2}}$? $3^{3}$ $3^{4}$ $3^{5}$ $3^{9}$

Explanation:

Step1: Simplify the fraction first

Use exponent rule $\frac{a^m}{a^n}=a^{m-n}$:
$\frac{3^3}{3^2}=3^{3-2}=3^1$

Step2: Multiply with the remaining term

Use exponent rule $a^m \cdot a^n=a^{m+n}$:
$3^4 \cdot 3^1=3^{4+1}=3^5$

Answer:

$3^5$ (the third option)