# Solve for m: (1/9)^m = 81^(m+4)

Neethu Nair | Certified Educator

Given:

(\frac{1}{9})^m=81^{m+4}

We have to find the value of m.

So we can write,

9^{-m}=(9^2)^{m+4}

i.e. 9^{-m}=9^{2m+8}

Comparing the left hand side and the right hand side we get,

-m=2m+8

i.e. -3m=8

which means m=\frac{-8}{3}

aishukul | Student

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:

9^-m=9^(2(m+4))

Cancel out the bases since they're the same number.

-m=2(m+4)

-m=2m+8

-8=3m

m=-8/3 This is the answer. You can also convert this into a decimal.

atyourservice | Student

(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

(1/9)^m =9^-m

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

to check

(1/9)^(-8/3) =350.5

81^((-8/3 + 4)) = 350.5