Question

Which of these choices show a pair of equivalent expressions? CHECK ALL THAT APPLY

Answer 1

Option C & D

Explanation:

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FACTS TO KNOW BEFORE SOLVING :-

Lets say there's an expression
`x^{(a)/(b) }` .

It can be also written it as →
`(\sqrt[b]{x} )^(a)` and vice-versa.

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Lets come to the question.

• In option A ,
  `7^{(5)/(7) }` can be also written as
  `(\sqrt[7]{7} )^(5)` . But it doesn't match with the other expression given. Hence they are not equivalent expressions.

• In option B ,
  `6^{(2)/(7) }` can be also written as
  `(\sqrt[7]{6} )^(2)` . But it doesn't match with the other expression given. Hence they are not equivalent expressions.

• In option C ,
  `5^{(3)/(2) }` can be also written as
  `(√(5) )^(3)`. Hence they are equivalent expressions.

• In option D ,
  `(\sqrt[4]{81} )^(5)` can be also written as
  `81^{(5)/(4) }` . Hence they are equivalent expressions

Thus , Option C & D are correct.