To solve this, first make both bases the same. 1/9^m is equivalent to 9^-m, and 9^2 equals 81 so the equation becomes:
Cancel out the bases since they're the same number.
m=-8/3 This is the answer. You can also convert this into a decimal.
`(1/9)^m = 81^(m+4)`
The first step to make this easier is to simplify the problems so that they have the same base.
We know that in order to make 1/9 a 9 we have to have a - for m because then we use the reciprocal
81 can be simplified as 9^2 therefore
`9^-m = 9^(2(m+4))`
Now set the exponent equal and solve:
Distribute the 2
`-m = 2m + 8`
move like terms to the same side:
`-3m = 8`
Divide by -3 to get m alone
`m = -8/3`
`-8/3` is the answer
`(1/9)^(-8/3) =350.5 `
`81^((-8/3 + 4)) = 350.5`