Question

Which expression is equivalent to (2^1/2*2^3/4)^2?

Answer 1

Answer: 4

Explanation:

Answer 2

`2^{(5)/(2)}`

Explanation:

We have to solve the given expression
`[(2)^{(1)/(2)}(2)^{(3)/(4)}]^(2)`

As we know [
`x^(a).x^(b)=x^(a+b)`]

Now by solving the given expression by this identity

`[2^{(1)/(2)+(3)/(4)}]^(2)`

=
`[2^{(5)/(4)}]^(2)`

=
`2^{((5)(2))/(4)}`

=
`2^{(10)/(4) }`

=
`2^{(5)/(2)}`

Therefore, the given expression can be represented by
`2^{(5)/(2)}`.