Only Two Numbers Present

Relevant wiki: Rules of Exponents

$\dfrac{6^9 × 9^6}{{\left(6 × 9\right)}^6} × 9 = 6x\\ \dfrac{6^9 × 9^6}{6^6 × 9^6} × 9 = 6x\\ {\dfrac{6^3\cancel{6^9} × \cancel{9^6}}{\cancel{6^6} × \cancel{9^6}}} × 9 = 6x\\ 6^3 × 9 = 6x\\ 6^2 × 9 = x\\ x = 36 × 9\\ x = \color{#69047E}{\boxed{324}}$

Relevant wiki: Rules of Exponents

$\dfrac{6^9 \times 9^6}{(6 \times 9)^6} \times 9 = 6x\\ \dfrac{6^3 \times 6^6 \times 9^6}{6^6 \times 9^6} \times 9 = 6x\\ 6^3 \times 9 = 6x\\ x=6^2 \times 9 = 36 \times 9 = \boxed{324}$

• 6^9 * 9^6 / (6*9)^6 = 6^6 * 9^6 *6^3/ 6^6 * 9^6 = 6^3.
• 6^3 * 9 = 6x
• (6^3 * 9) / 6 = x
• 6^2 * 9 = x = 6 *6 *9 = 324

$\frac{6^9 \times 9^6}{(6 \times 9)^6} \times 9=6x \implies \frac{6^9 \times 9^6}{6^6 \times 9^6} \times 9 \implies \frac{6^3 \times 6^6 \times 9^6}{6^6 \times 9^6} \times 9 \implies 6^3 \times 9=6x \implies 6^2 \times 9=x \implies x=\boxed{\large{324}}$