Question

Please select the best answer from the choices provided

Answer 1

The correct answer option is b. 2.

Explanation:

We are given an expression
`2^{(1)/(2)  }.2^{(1)/(2)  }` and we are supposed to simplify it.

We know that
`a^b.a^c= a^(b+c)` which means if the bases are same, then the exponents are added up.

So here, our bases are same i.e. 2 so we will add up the exponents to get:

`2^{(1)/(2)+ (1)/(2)  }`

Taking the LMC of the exponents to get:

`2^{(1+1)/(4)  }`

`2^{(2)/(2)  }`

The fraction in the exponent gets cancelled so we are left with 2.

Answer 2

we are given

`2^{(1)/(2)}\cdot 2^{(1)/(2) }`

we can use exponent formula

`a^n \cdot a^m=a^(n+m)`

now, we can use this formula

`2^{(1)/(2)}\cdot 2^{(1)/(2) }=2^{(1)/(2)+(1)/(2) }`

we can add exponent

and we get

`2^{(1)/(2)}\cdot 2^{(1)/(2) }=2^{(1+1)/(2) }`

`2^{(1)/(2)}\cdot 2^{(1)/(2) }=2^{(2)/(2) }`

`2^{(1)/(2)}\cdot 2^{(1)/(2) }=2^(1)`

`2^{(1)/(2)}\cdot 2^{(1)/(2) }=2`

So, option-B.......Answer