Finite Math Examples

${(\sqrt[4]{3 x})}^{7}$

Step 1

Rewrite ${\sqrt[4]{3 x}}^{7}$ as $\sqrt[4]{{(3 x)}^{7}}$ .

$\sqrt[4]{{(3 x)}^{7}}$

Step 2

Apply the product rule to $3 x$ .

$\sqrt[4]{3^{7} x^{7}}$

Step 3

Raise $3$ to the power of $7$ .

$\sqrt[4]{2187 x^{7}}$

Step 4

Rewrite $2187 x^{7}$ as ${(3 x)}^{4} \cdot (27 x^{3})$ .

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Step 4.1

Factor $81$ out of $2187$ .

$\sqrt[4]{81 (27) x^{7}}$

Step 4.2

Rewrite $81$ as $3^{4}$ .

$\sqrt[4]{3^{4} \cdot 27 x^{7}}$

Step 4.3

Factor out $x^{4}$ .

$\sqrt[4]{3^{4} \cdot 27 (x^{4} x^{3})}$

Step 4.4

Move $27$ .

$\sqrt[4]{3^{4} x^{4} \cdot 27 x^{3}}$

Step 4.5

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

$\sqrt[4]{{(3 x)}^{4} \cdot 27 x^{3}}$

Step 4.6

Add parentheses.

$\sqrt[4]{{(3 x)}^{4} \cdot (27 x^{3})}$

Step 5

Pull terms out from under the radical.

$3 x \sqrt[4]{27 x^{3}}$