How do I simplify $6 \cdot 9^{\frac{3x-1} 2}$ into $a \cdot b^x$?

Question

How do I simplify $6 \cdot 9^{\tfrac{3x-1} 2}$ into $a \cdot b^x$? I've been unable to understand how so far. Thanks.

Answer 1

$$y=6(9)^{\frac{3x-1}{2}}=6(9)^{\frac{3x}{2}}(9)^{-\frac{1}{2}}=\frac{6(9^{\frac{1}{2}})^{3x}}{9^{\frac{1}{2}}}=\frac{6(3)^{3x}}{3}=2(27)^x$$

Answer 2

$$y(x)=6\cdot9^{\frac{3x-1}{2}}=2\cdot3^1\cdot3^{\frac{3x-1}{2}}\cdot3^{\frac{3x-1}{2}}=2\cdot3^{1+\frac{3x-1}{2}+\frac{3x-1}{2}}=2\cdot3^{3x}$$