Question

What expression is equivalent to [x1/4*y16]^1/2

Answer 1

The given expression is
`{{{\bf x}^{(\bf 1)/(\bf 4)}* y^(\bf 16)}} ^ {(1)/(2)} =x^{\frac {\bf 1}{\bf 8}}* y^(\bf 4)`.

Explanation:

The given expression is
`{{x^{(1)/(4)}* y^(16)}}^(1)/(2)`

`{{x^{(1)/(4)}* y^(16)}}^{(1)/(2)}=\sqrt{x^{(1)/(4)}* y^(16)}`

`{{x^{(1)/(4)}* y^(16)}}^{(1)/(2)}= \sqrt{x^{(1)/(4)}}* \sqrt{y^(16)}`

`{{x^{(1)/(4)}* y^(16)}}^{(1)/(2)}=x^{(1)/(4)}^(1)/(2)} * y^(4)`

`{{x^{(1)/(4)}* y^(16)}}^{(1)/(2)}= x^{(1)/(8)}* y^(4)` by using
`{a^(m)} ^(n)=a^ {mn}` property.