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9 to the power n *3 to the power -m upon 2*-2 — 27 to the power n upon 3 to the power 3m *2 to the power 3 = 1 upon 27. Pls answer this kindly follow the exact ques ?
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9 to the power n *3 to the power -m upon 2*-2 — 27 to the power n upon...
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9 to the power n *3 to the power -m upon 2*-2 — 27 to the power n upon...
Solving the given expression

Given expression:

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

Simplifying the expression:

9^n * 3^(-m) * 2^2 / 1 - 27^n / (3^3m * 2^3) = 1/27 [using 2^-2 = 1/2^2 = 1/4]

9^n * 3^(-m) * 4 / 1 - 27^n / (3^3m * 2^3) = 1/27 [using 2^2 = 4]

9^n * 3^(-m) * 4 / 1 - 3^(3m) * 3^n / (3^(3m) * 2^3) = 1/27 [using 27 = 3^3]

9^n * 3^(-m) * 4 / 1 - 3^(3m-n) / 8 = 1/27 [using a^m / a^n = a^(m-n)]

Multiplying both sides by 27:

9^n * 3^(-m) * 108 - 27^(n-3m) / 8 = 1

9^n * 3^(-m) * 864 - 27^(n-3m) = 8

9^n * 3^(-m) * 3^3 * 288 - 27^(n-3m) = 8 [using 864 = 3^3 * 288]

3^n * 3^(-m) * 27^(n-3m) * 288 - 27^(n-3m) = 8 [using 9 = 3^2]

3^(n-m) * 27^(n-3m) * 288 - 27^(n-3m) = 8

3^(n-m) * 27^(n-3m) * 288 - 27^(n-3m) * 1 = 8

Let x = 27^(n-3m). Then we have:

3^(n-m) * 288x - x = 8

3^(n-m) * 288x = x + 8

3^(n-m) * 288x = (x/8) + 1

Substituting back x = 27^(n-3m):

3^(n-m) * 288 * 27^(n-3m) = (1/8) * 27^(n-3m) + 1

3^(n-m) * 3^(3n-9m) * 288 = (1/8) * 3^(3n-9m) + 1

3^(4n-10m) * 288 = (1/8) * 3^(3n-9m) + 1

3^(4n-10m) * 288 = 3^(3n-9m-3) / 8 + 1

Multiplying both sides by 8:

3^(4n-10m)
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9 to the power n *3 to the power -m upon 2*-2 — 27 to the power n upon 3 to the power 3m *2 to the power 3 = 1 upon 27. Pls answer this kindly follow the exact ques ?
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