Final answer:
The expression (4th root of y⁵)¹⁄² can be rewritten as y5/8, by using properties of exponents and radicals.
Step-by-step explanation:
To rewrite the expression (4th root of y⁵)¹⁄² in the form of k·yⁿ, we need to apply properties of exponents and radicals. First, we recall that the fourth root of y5 can be written as y5/4.
Then, we are raising that result to the power of 1/2, so we multiply the exponents (5/4) and (1/2), which gives us y5/8. The expression does not have a numerical coefficient other than 1 (or y0), so the final expression is simply y5/8.