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D.  ∛4a^2 / a

Step-by-step explanation:

∛4a / ∛a^2

= ∛(4a)* ∛a / ∛a^2 * ∛a

= ∛4a^2 / ∛a^3

= ∛4a^2 / a

Answer is D.  ∛4a^2 / a

d     4 ^1/3 a^2/3

    a

Step-by-step explanation:

(4a) ^ 1/3

( a^2) ^ 1/3

We know  that (bc)^d = b^d * c^d   and m^n^p = m^(n+p)

(4) ^ 1/3 * (a) ^ 1/3

( a) ^(2* 1/3)

(4) ^ 1/3 * (a) ^ 1/3

( a) ^(2/3)

We know that when we divide powers with the same base, we subtract the exponents

(4) ^ 1/3 * (a) ^ (1/3 - 2/3)

4 ^ (1/3) * a ^ -1/3

4 ^1/3

a^ 1/3

We can multiply the top and bottom by a^2/3

4 ^1/3 a^2/3

a^ 1/3 * a^2/3

4 ^1/3 a^2/3

a