Question

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

Answer 1

`\large\boxed{√(2^5)}`

Explanation:

`\bigg(2^(1)/(2)\cdot2^(3)/(4)\bigg)^2\qquad\text{use}\ a^n\cdot a^m\\\\=\bigg(2^{(1)/(2)+(3)/(4)}\bigg)^2\qquad\left/(1)/(2)+(3)/(4)=(1\cdot2)/(2\cdot2)+(3)/(4)=(2)/(4)+(3)/(4)=(5)/(4)\right/\\\\=\bigg(2^(5)/(4)\bigg)^2\qquad\text{use}\ (a^n)^m=a^(nm)\\\\=2^{(5)/(4)\cdot2}\\\\=2^{(5)/(2)}\qquad\text{use}\ a^(m)/(n)=\sqrt[n]{a^m}\\\\=√(2^5)`

Answer 2

`√(2^5)`

Explanation:

`2^(1/2)` ×
`2^(3/4)` =
`2^(5/4)`

(
`2^(5/4)`)² =
`2^(5/2)` =
`√(2^5)`