Question

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

Answer 1

(2^1/2 x 2^3/4)^2
= (2^2/4 x 2^3/4)^2
= (2^5/4)^2
= 2^10/4
= 2^5/2

Answer 2

Given the expression:
`(2^{(1)/(2)} * 2^{(3)/(4)})^2`

Using:

• 
  `a^n * a^m = a^(n+m)`

• 
  `(a^n)^m = a^(nm)`
• 
  `a^{(m)/(n)} = \sqrt[n]{a^m}`

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

Simplify:

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

`2^{(5 * 2)/(4)} =2^{ (5)/(2)}` =
`\sqrt[2]{2^5} = \sqrt[2]{32} = 4√(2)`

Therefore, the expression which is equivalent to
`(2^{(1)/(2)} * 2^{(3)/(4)})^2` is:
`4√(2)` or
`2^{(5)/(2) }`