Algebra Examples

$\sqrt{16 x^{4}} \cdot \sqrt[4]{16 x^{2}}$

Step 1

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

$\sqrt{{(4 x^{2})}^{2}} \cdot \sqrt[4]{16 x^{2}}$

Step 2

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

$4 x^{2} \cdot \sqrt[4]{16 x^{2}}$

Step 3

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

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

Step 4

Pull terms out from under the radical.

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

Step 5

Rewrite $\sqrt[4]{x^{2}}$ as $\sqrt{\sqrt{x^{2}}}$ .

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

Step 6

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

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

Step 7

Multiply $2$ by $4$ .

$8 x^{2} \sqrt{x}$