Simplify (3 square root of x)(4 cube root of x^2)

$(3 \sqrt{x}) (4 \sqrt[3]{x^{2}})$

Step 1

Multiply $(3 \sqrt{x}) (4 \sqrt[3]{x^{2}})$ .

Multiply $4$ by $3$ .

$12 \sqrt{x} \sqrt[3]{x^{2}}$

Rewrite the expression using the least common index of $6$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x^{2}}$ as $x^{\frac{2}{3}}$ .

$12 (x^{\frac{2}{3}} \sqrt{x})$

Rewrite $x^{\frac{2}{3}}$ as $x^{\frac{4}{6}}$ .

$12 (x^{\frac{4}{6}} \sqrt{x})$

Rewrite $x^{\frac{4}{6}}$ as $\sqrt[6]{x^{4}}$ .

$12 (\sqrt[6]{x^{4}} \sqrt{x})$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

$12 (\sqrt[6]{x^{4}} x^{\frac{1}{2}})$

Rewrite $x^{\frac{1}{2}}$ as $x^{\frac{3}{6}}$ .

$12 (\sqrt[6]{x^{4}} x^{\frac{3}{6}})$

Rewrite $x^{\frac{3}{6}}$ as $\sqrt[6]{x^{3}}$ .

$12 (\sqrt[6]{x^{4}} \sqrt[6]{x^{3}})$

Combine using the product rule for radicals.

$12 \sqrt[6]{x^{4} x^{3}}$

Multiply $x^{4}$ by $x^{3}$ by adding the exponents.

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

$12 \sqrt[6]{x^{4 + 3}}$

Add $4$ and $3$ .

$12 \sqrt[6]{x^{7}}$

Step 2

Factor out $x^{6}$ .

$12 \sqrt[6]{x^{6} x}$

Step 3

Pull terms out from under the radical.

$12 x \sqrt[6]{x}$