Question

For what value does (1/9)^a+1=81^a+1 12^2-a?

Answer 1

Answer:

a = -4

Step-by-step explanation:

$(\dfrac{1}{9})^{a + 1} = 81^{a + 1} \cdot 27^{2 - a}$

$(3^{-2})^{a + 1} = (3^4)^{a + 1} \cdot (3^3)^{2 - a}$

$3^{-2a - 2} = 3^{4a + 4} \cdot 3^{6 - 3a}$

$3^{-2a - 2} = 3^{4a + 4 + 6 - 3a}$

$3^{-2a - 2} = 3^{a + 10}$

$-2a - 2 = a + 10$

$-3a = 12$

$a = -4$