Algebra Examples

$\sqrt[3]{64 x^{4}} \cdot \sqrt{16 x}$

Step 1

Rewrite $64 x^{4}$ as ${(4 x)}^{3} x$ .

Tap for more steps...

Step 1.1

Rewrite $64$ as $4^{3}$ .

$\sqrt[3]{4^{3} x^{4}} \cdot \sqrt{16 x}$

Step 1.2

Factor out $x^{3}$ .

$\sqrt[3]{4^{3} (x^{3} x)} \cdot \sqrt{16 x}$

Step 1.3

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

$\sqrt[3]{{(4 x)}^{3} x} \cdot \sqrt{16 x}$

Step 2

Pull terms out from under the radical.

$4 x \sqrt[3]{x} \cdot \sqrt{16 x}$

Step 3

Rewrite $16 x$ as ${(2^{2})}^{2} x$ .

Tap for more steps...

Step 3.1

Rewrite $16$ as $4^{2}$ .

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

Step 3.2

Rewrite $4$ as $2^{2}$ .

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

Step 4

Pull terms out from under the radical.

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

Step 5

Raise $2$ to the power of $2$ .

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

Step 6

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

Tap for more steps...

Step 6.1

Multiply $4$ by $4$ .

$16 x \sqrt[3]{x} \sqrt{x}$

Step 6.2

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

Tap for more steps...

Step 6.2.1

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

$16 x (x^{\frac{1}{2}} \sqrt[3]{x})$

Step 6.2.2

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

$16 x (x^{\frac{3}{6}} \sqrt[3]{x})$

Step 6.2.3

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

$16 x (\sqrt[6]{x^{3}} \sqrt[3]{x})$

Step 6.2.4

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x}$ as $x^{\frac{1}{3}}$ .

$16 x (\sqrt[6]{x^{3}} x^{\frac{1}{3}})$

Step 6.2.5

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

$16 x (\sqrt[6]{x^{3}} x^{\frac{2}{6}})$

Step 6.2.6

Rewrite $x^{\frac{2}{6}}$ as $\sqrt[6]{x^{2}}$ .

$16 x (\sqrt[6]{x^{3}} \sqrt[6]{x^{2}})$

Step 6.3

Combine using the product rule for radicals.

$16 x \sqrt[6]{x^{3} x^{2}}$

Step 6.4

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

Tap for more steps...

Step 6.4.1

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

$16 x \sqrt[6]{x^{3 + 2}}$

Step 6.4.2

Add $3$ and $2$ .

$16 x \sqrt[6]{x^{5}}$