Question

For what value of a does (1/9)^a+1 =81^a+1 x 27^2-a ?

-4
-2
2
6

Answer 1

the answer to the question you is A on edg

Explanation:

Answer 2

- 4

Explanation:

Using the rule of exponents

•
`a^(m)` ×
`a^(n)` ⇔
`a^((m+n))`

•
`a^(-m)` ⇔
`(1)/(a^(m) )`

`((1)/(9)) ^(a+1)` =
`9^(-(a+1))` =
`3^(-2(a+1))`

and right side

=
`3^(4(a+1))` ×
`3^(3(2-a))`

Hence

`3^(-2a-2)` =
`3^(4a+4)` ×
`3^(6-3a)`

`3^(-2a-2)` =
`3^(a+10)`

Equating exponents on both sides gives

a + 10 = - 2a - 2 ( add 2a to both sides )

3a + 10 = - 2 (subtract 10 from both sides )

3a = - 12 ( divide both sides by 3 )

a = - 4