Simplify fourth root of 27x* fourth root of 3x^3

$\sqrt[4]{27 x} \cdot \sqrt[4]{3 x^{3}}$

Step 1

Multiply $\sqrt[4]{27 x} \sqrt[4]{3 x^{3}}$ .

Combine using the product rule for radicals.

$\sqrt[4]{27 x (3 x^{3})}$

Multiply $3$ by $27$ .

$\sqrt[4]{81 x \cdot x^{3}}$

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

Move $x^{3}$ .

$\sqrt[4]{81 (x^{3} x)}$

Multiply $x^{3}$ by $x$ .

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

$\sqrt[4]{81 (x^{3} x^{1})}$

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

$\sqrt[4]{81 x^{3 + 1}}$

Add $3$ and $1$ .

$\sqrt[4]{81 x^{4}}$

Step 2

Rewrite $81 x^{4}$ as ${(3 x)}^{4}$ .

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

Step 3

Pull terms out from under the radical, assuming positive real numbers.

$3 x$