Answer:
a = -4
Step-by-step explanation:
[tex] (\dfrac{1}{9})^{a + 1} = 81^{a + 1} \cdot 27^{2 - a} [/tex]
[tex] (3^{-2})^{a + 1} = (3^4)^{a + 1} \cdot (3^3)^{2 - a} [/tex]
[tex] 3^{-2a - 2} = 3^{4a + 4} \cdot 3^{6 - 3a} [/tex]
[tex] 3^{-2a - 2} = 3^{4a + 4 + 6 - 3a} [/tex]
[tex] 3^{-2a - 2} = 3^{a + 10} [/tex]
[tex] -2a - 2 = a + 10 [/tex]
[tex] -3a = 12 [/tex]
[tex] a = -4 [/tex]
