Math, asked by harinikota7b, 1 day ago

(27^-3/9^-3)^1/5 please give a detailed solution

Answers

Answered by mahakulkarpooja615
0

Answer:

The value of  (\frac{27^{-3} }{9^{-3}})^{\frac{1}{5}  } is 3^{-\frac{3}{5} } .

Step-by-step explanation:

Given : (\frac{27^{-3} }{9^{-3}})^{\frac{1}{5}  }

To find : Value of the above expression.

Solution :

  • The given expression is,  (\frac{27^{-3} }{9^{-3}})^{\frac{1}{5}  }
  • We know the exponential rules,

       \frac{a^{m} }{b^{m}}=\frac{a}{b}^{m}

  • Using this rule in given expression, we get

      (\frac{27^{-3} }{9^{-3}})^{\frac{1}{5}  } = [(\frac{27}{9})^{-3} ] ^{\frac{1}{5} }

                = (3^{-3})^{\frac{1}{5}}

  • Now, another rule is,

        (a^{m} )^{n} = a^{m*n}

  • Using this rule in above expression, we get

           = 3^{-3*\frac{1}{5} }

           = 3^{-\frac{3}{5} }

  • ∴ The value of  (\frac{27^{-3} }{9^{-3}})^{\frac{1}{5}  } is 3^{-\frac{3}{5} }.
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