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27n=1327^n = \frac{1}{3}

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Full solution

Q. 27n=1327^n = \frac{1}{3}
  1. Rewrite as Power of 33: Rewrite 2727 as a power of 33: 27=3327 = 3^3.\newlineSo, 27n=(33)n27^n = (3^3)^n.
  2. Simplify Exponent: Simplify the exponent: (33)n=33n(3^3)^n = 3^{3n}.\newlineNow we have 33n=133^{3n} = \frac{1}{3}.
  3. Rewrite as Same Base: Rewrite 13\frac{1}{3} as 3−13^{-1} to have the same base: 33n=3−13^{3n} = 3^{-1}.
  4. Set Exponents Equal: Set the exponents equal to each other since the bases are the same: 3n=−13n = -1.
  5. Solve for n: Solve for n: n=−13n = -\frac{1}{3}.

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