Finite Math Examples

$\sqrt[4]{48 x^{16} w^{17}}$

Step 1

Rewrite $48 x^{16} w^{17}$ as ${(2 x^{4} w^{4})}^{4} \cdot (3 w)$ .

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Step 1.1

Factor $16$ out of $48$ .

$\sqrt[4]{16 (3) x^{16} w^{17}}$

Step 1.2

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

$\sqrt[4]{2^{4} \cdot 3 x^{16} w^{17}}$

Step 1.3

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

$\sqrt[4]{2^{4} \cdot 3 {(x^{4})}^{4} w^{17}}$

Step 1.4

Factor out $w^{16}$ .

$\sqrt[4]{2^{4} \cdot 3 {(x^{4})}^{4} (w^{16} w)}$

Step 1.5

Rewrite $w^{16}$ as ${(w^{4})}^{4}$ .

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

Step 1.6

Move $3$ .

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

Step 1.7

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

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

Step 1.8

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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