(x ^ (3/4))(y ^ (1/4)) = 4th root ((x^3) y)
Explanation:
- The numerator of the exponential is kept where it is whereas when converting an exponential into a radical, the denominator becomes the root of the variable.
- (x ^ (3/4)) will be equal to the [tex]4^{th}[/tex] root of the value x ^ 3 i.e. [tex]\sqrt[4]{x^3}[/tex].
- (y ^ (1/4)) will also be equal to the [tex]4^{th}[/tex] root of y's value i.e. [tex]\sqrt[4]{y}[/tex].
- Out of the given options, options 1, 3 and 4 have cube roots so they cannot be the answers. Option 2 has the value of x correct but the value of y will equal y ^ (1/2) so it is also incorrect.
- So the [tex]5^{th}[/tex] option is the right answer.
