Given that $2\times 3^a +b=27$ and $b=3^a$ , find the value of $ab$ .

The answer is 18.

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$2 \times 3^a + b = 27 \cdots (1)$

$b=3^a \cdots (2)$

Sub $(2)$ into $(1)$ : $2b+b=27 \implies b=9$

Sub $b=9$ into $(2)$ : $9=3^a \implies a=2$

Hence $ab=2(9)=\boxed{18}$ .