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c) root(3)((27^(2x-1))/(3^(x+1)))=9

c) 272x−13x+13=9 \sqrt[3]{\frac{27^{2 x-1}}{3^{x+1}}}=9

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Simplify the product of two radical expressions having same variableright chevron icon

Full solution

Q. c) 272x−13x+13=9 \sqrt[3]{\frac{27^{2 x-1}}{3^{x+1}}}=9
  1. Rewrite Equation: Rewrite the equation using radical notation.\newline272x−13x+13=9\sqrt[3]{\frac{27^{2x-1}}{3^{x+1}}} = 9
  2. Express 2727 as 333^3: Express 2727 as 333^3 and simplify the exponent inside the radical.(333x+1)2x−13=9\sqrt[3]{\left(\frac{3^3}{3^{x+1}}\right)^{2x-1}} = 9
  3. Apply Power Rule: Apply the power rule am∗n=(am)na^{m*n} = (a^m)^n to the numerator.(33∗(2x−1)3x+1)3=9\sqrt[3]{\left(\frac{3^{3*(2x-1)}}{3^{x+1}}\right)} = 9
  4. Simplify Exponent: Simplify the exponent in the numerator. 36x−33x+13=9\sqrt[3]{\frac{3^{6x-3}}{3^{x+1}}} = 9
  5. Combine Exponents: Combine the exponents over the common base inside the radical. 36x−3−x−13=9\sqrt[3]{3^{6x-3-x-1}} = 9
  6. Simplify Exponent: Simplify the exponent by subtracting. 35x−43=9\sqrt[3]{3^{5x-4}} = 9
  7. Express 99 as 323^2: Express 99 as 323^2.35x−43=32\sqrt[3]{3^{5x-4}} = 3^2
  8. Equate Exponents: Since both sides of the equation are now under the same root, we can equate the exponents. 5x−4=2×35x - 4 = 2 \times 3

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