Solve the following exercise:

$\sqrt[4]{\sqrt[3]{3}}=$

To simplify the given expression, we will use two laws of exponents:

__A.__ Definition of the root as an exponent:

$\sqrt[n]{a}=a^{\frac{1}{n}}$

__B.__ Law of exponents for an exponent on an exponent:

$(a^m)^n=a^{m\cdot n}$

**Let's begin** simplifying the given expression:

$\sqrt[4]{\sqrt[3]{3}}= \\$We will use the law of exponents shown in __A__ and **first **__convert__ the roots in the expression **to exponents**, we will do this in two steps - in the first step **we will convert the inner root** in the expression and in the next step **we will convert the outer root**:

$\sqrt[4]{\sqrt[3]{3}}= \\
\sqrt[4]{3^{\frac{1}{3}}}= \\
(3^{\frac{1}{3}})^{\frac{1}{4}}=$We continue and use the law of exponents shown in __B__ for __performing the exponent on the term (in parentheses) which is in the exponent__, then we will perform **the multiplication of the exponents** which are in the exponent term:

$(3^{\frac{1}{3}})^{\frac{1}{4}}= \\
3^{\frac{1}{3}\cdot\frac{1}{4}}=\\
3^{\frac{1\cdot1}{3\cdot4}}=\\
\boxed{3^{\frac{1}{12}}}=\\
\boxed{\sqrt[12]{3}}$ In the final step **we return to writing the root**, that is - __back__, using the law of exponents shown in __A__ (__in the opposite direction__),

**Let's summarize** the simplification of the given expression:

$\sqrt[4]{\sqrt[3]{3}}= \\
(3^{\frac{1}{3}})^{\frac{1}{4}}= \\
\boxed{3^{\frac{1}{12}}}=\\
\boxed{\sqrt[12]{3}}$__Therefore, note that the correct answer (most) is answer D__.