Question

Which of the following is equivalent to (16^3/2)^1/2? 6 8 12 64

Answer 1

`\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^( n)} \qquad \qquad \sqrt[{ m}]{a^( n)}\implies a^{\frac{{ n}}{{ m}}}\\\\ -------------------------------\\\\ \left( 16^{(3)/(2)} \right)^{(1)/(2)}\implies 16^{(3)/(2)\cdot (1)/(2)}\implies 16^{(3)/(4)}\qquad \boxed{16=2^4}\qquad (2^4)^{(3)/(4)}\implies 2^{4\cdot (3)/(4)} \\\\\\ 2^3\implies 8`

Answer 2

Option B is correct that is 8.

Explanation:

Given Expression :
`(16^{(3)/(2)})^{(1)/(2)}`

We use a law of exponent here to simplify it,

`(x^a)^b=x^(ab)`

Consider,

`(16^{(3)/(2)})^{(1)/(2)}`

`=16^{(3)/(2)*(1)/(2)}`

`=16^{(3)/(4)}`

`=(2^4)^{(3)/(4)}`

`=2^{4*(3)/(4)}`

`=2^3`

`=8`

Therefore, Option B is correct that is 8.