Simplify 3 fourth root of 18a^9* fourth root of 6ab^2

$3 \sqrt[4]{18 a^{9}} \cdot \sqrt[4]{6 a b^{2}}$

Rewrite $18 a^{9}$ as ${(a^{2})}^{4} \cdot (18 a)$ .

Factor out $a^{8}$ .

$3 \sqrt[4]{18 (a^{8} a)} \cdot \sqrt[4]{6 a b^{2}}$

Rewrite $a^{8}$ as ${(a^{2})}^{4}$ .

$3 \sqrt[4]{18 ({(a^{2})}^{4} a)} \cdot \sqrt[4]{6 a b^{2}}$

Reorder $18$ and ${(a^{2})}^{4}$ .

$3 \sqrt[4]{{(a^{2})}^{4} \cdot 18 a} \cdot \sqrt[4]{6 a b^{2}}$

Add parentheses.

$3 \sqrt[4]{{(a^{2})}^{4} \cdot (18 a)} \cdot \sqrt[4]{6 a b^{2}}$

Pull terms out from under the radical.

$3 (a^{2} \sqrt[4]{18 a}) \cdot \sqrt[4]{6 a b^{2}}$

Multiply $3 a^{2} \sqrt[4]{18 a} \sqrt[4]{6 a b^{2}}$ .

Combine using the product rule for radicals.

$3 a^{2} \sqrt[4]{6 a b^{2} (18 a)}$

Multiply $18$ by $6$ .

$3 a^{2} \sqrt[4]{108 a b^{2} a}$

Raise $a$ to the power of $1$ .

$3 a^{2} \sqrt[4]{108 (a^{1} a) b^{2}}$

Raise $a$ to the power of $1$ .

$3 a^{2} \sqrt[4]{108 (a^{1} a^{1}) b^{2}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 a^{2} \sqrt[4]{108 a^{1 + 1} b^{2}}$

Add $1$ and $1$ .

$3 a^{2} \sqrt[4]{108 a^{2} b^{2}}$