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Question

Evaluate:       $${ 3 }^{ 3 }\times { \left( 243 \right)  }^{ -\frac { 2 }{ 3 }  }\times { 9 }^{ -\frac { 1 }{ 3 }  }$$


Solution

Let $$a={3}^{3}\times {\left({3}^{5}\right)}^{\frac{-2}{3}}\times{\left({3}^{2}\right)}^{\frac{-1}{3}}$$

         $$={3}^{3}\times{3}^{\frac{-10}{3}}\times{3}^{\frac{-2}{3}}$$

         $$={3}^{3-\frac{10}{3}-\frac{2}{3}}$$

         $$={3}^{3-\frac{12}{3}}$$

         $$={3}^{3-4}$$

         $$={3}^{-1}$$

$$a=\dfrac{1}{3}$$

$$\therefore {3}^{3}\times {\left({3}^{5}\right)}^{\frac{-2}{3}}\times{\left({3}^{2}\right)}^{\frac{-1}{3}}=\dfrac{1}{3}$$

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