Solve 9^n*3^2*3^n-27^n/3^3m*2^3=1/27

Evaluate

9^{n} \times 3^{2} \times 3^{n} - \frac{2 7 ^{n}}{3 ^{3}} \times m \times 2^{3} = \frac{1}{27}

Simplify

More Steps

3^{3 n + 2} - 8 \times 2 7^{n - 1} m = \frac{1}{27}

Move the expression to the right-hand side and change its sign

- 8 \times 2 7^{n - 1} m = \frac{1}{27} - 3^{3 n + 2}

Subtract the terms

More Steps

- 8 \times 2 7^{n - 1} m = \frac{1 - 3 ^{3 n + 5}}{27}

Multiply by the reciprocal

- 8 \times 2 7^{n - 1} m (- \frac{1}{8 \times 2 7 ^{n - 1}}) = \frac{1 - 3 ^{3 n + 5}}{27} \times (- \frac{1}{8 \times 2 7 ^{n - 1}})

Multiply

m = \frac{1 - 3 ^{3 n + 5}}{27} \times (- \frac{1}{8 \times 2 7 ^{n - 1}})

Solution

More Steps

m = \frac{- 1 + 3 ^{3 n + 5}}{216 \times 2 7 ^{n - 1}}

Solve the equation