Question

Which expression is equivalent to (3√x^2)^6

Answer 1

Explanation:

`= {(3 \sqrt{ {x}^(2) } )}^(6)`

`= {(3 {x}^{ (2)/(2) } )}^(6)`

`= {(3x)}^(6)`

`= {3}^(6) {x}^(6)`

`= 729 {x}^(6)`

Answer 2

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`\large \sf \underline{Problem:}`

Which expression is equivalent to (3√x^2)^6

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`\large \sf \underline{Answer:}`

The answer is x⁴

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`\large \sf \underline{Explanation:}`

`( \sqrt[3] {x}^(2) )⁶ \: {The \: cube \: root \: of \: x² \: is \: x^(2/3)} (x^(2/3))⁶ {Now, \: simply \: multiply \: 2/3 \: by \: 6 \: to \: get \: 4.}`

x⁴

`( \sqrt[3] {x}^(2) )⁶ \: is \: equivalent \: to \: x⁴`

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