Precalculus Examples

$\sqrt[3]{54 x^{17}}$

Step 1

Rewrite $54 x^{17}$ as ${(3 x^{5})}^{3} \cdot (2 x^{2})$ .

Tap for more steps...

Step 1.1

Factor $27$ out of $54$ .

$\sqrt[3]{27 (2) x^{17}}$

Step 1.2

Rewrite $27$ as $3^{3}$ .

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

Step 1.3

Factor out $x^{15}$ .

$\sqrt[3]{3^{3} \cdot 2 (x^{15} x^{2})}$

Step 1.4

Rewrite $x^{15}$ as ${(x^{5})}^{3}$ .

$\sqrt[3]{3^{3} \cdot 2 ({(x^{5})}^{3} x^{2})}$

Step 1.5

Move $2$ .

$\sqrt[3]{3^{3} {(x^{5})}^{3} \cdot 2 x^{2}}$

Step 1.6

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

$\sqrt[3]{{(3 x^{5})}^{3} \cdot 2 x^{2}}$

Step 1.7

Add parentheses.

$\sqrt[3]{{(3 x^{5})}^{3} \cdot (2 x^{2})}$

Step 2

Pull terms out from under the radical.

$3 x^{5} \sqrt[3]{2 x^{2}}$