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.
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1@highlandertf2: How about $6 \cdot 9^{\tfrac{3x-1} 2} = 6 \cdot 3^{3x-1} = 6 \cdot 3^{3x} \cdot 3^{-1} = 2 \cdot (3^{3})^x = 2 \cdot 27^x$ ? – Moritz Sep 26 '16 at 16:23
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$$y=6(9)^{\frac{3x-1}{2}}=6(9)^{\frac{3x}{2}}(9)^{-\frac{1}{2}}=\frac{6(9^{\frac{1}{2}})^{3x}}{9^{\frac{1}{2}}}=\frac{6(3)^{3x}}{3}=2(27)^x$$
E.H.E
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$$y(x)=6\cdot9^{\frac{3x-1}{2}}=2\cdot3^1\cdot3^{\frac{3x-1}{2}}\cdot3^{\frac{3x-1}{2}}=2\cdot3^{1+\frac{3x-1}{2}+\frac{3x-1}{2}}=2\cdot3^{3x}$$
Jan Eerland
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