Question

The product cube root of 2 x square root of 4 x 12th root of 32 is equal to: ?

Answer 1

cubed root of 2:
`\sqrt[3]{2}` =
`2^{(1)/(3)}`

square root of 4:
`√(4)` = 2¹

12th root of 32:
`\sqrt[12]{32}` =
`\sqrt[12]{2^(5)}` =
`2^{(5)/(12)}`

`2^{(1)/(3)}` x 2¹ x
`2^{(5)/(12)}` =
`2^{(1)/(3) + 1 + (5)/(12) }` =
`2^{(4)/(12) + (12)/(12) + (5)/(12) }` =
`2^{(21)/(12)}` =
`2^{(7)/(4)}` = 2
`\sqrt[4]{2^(3)}` = 2
`\sqrt[4]{8}`

Answer: 2
`\sqrt[4]{8}`