Algebra Examples

$\sqrt{16 x^{2}} \cdot x^{\frac{2}{3}} + \sqrt[3]{8 x^{5}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $16 x^{2}$ as ${(4 x)}^{2}$ .

$\sqrt{{(4 x)}^{2}} \cdot x^{\frac{2}{3}} + \sqrt[3]{8 x^{5}}$

Step 1.2

Pull terms out from under the radical.

$| 4 x | \cdot x^{\frac{2}{3}} + \sqrt[3]{8 x^{5}}$

Step 1.3

Remove non-negative terms from the absolute value.

$4 | x | \cdot x^{\frac{2}{3}} + \sqrt[3]{8 x^{5}}$

Step 1.4

Rewrite $8 x^{5}$ as ${(2 x)}^{3} x^{2}$ .

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Step 1.4.1

Rewrite $8$ as $2^{3}$ .

$4 | x | x^{\frac{2}{3}} + \sqrt[3]{2^{3} x^{5}}$

Step 1.4.2

Factor out $x^{3}$ .

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

Step 1.4.3

Rewrite $2^{3} x^{3}$ as ${(2 x)}^{3}$ .

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

Step 1.5

Pull terms out from under the radical.

$4 | x | x^{\frac{2}{3}} + 2 x \sqrt[3]{x^{2}}$

Step 2

Reorder factors in $4 | x | x^{\frac{2}{3}} + 2 x \sqrt[3]{x^{2}}$ .

$4 x^{\frac{2}{3}} | x | + 2 x \sqrt[3]{x^{2}}$