Algebra Examples

$\sqrt[4]{{(30 x^{2})}^{3}}$

Step 1

Apply the product rule to $30 x^{2}$ .

$\sqrt[4]{30^{3} {(x^{2})}^{3}}$

Step 2

Raise $30$ to the power of $3$ .

$\sqrt[4]{27000 {(x^{2})}^{3}}$

Step 3

Multiply the exponents in ${(x^{2})}^{3}$ .

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Step 3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\sqrt[4]{27000 x^{2 \cdot 3}}$

Step 3.2

Multiply $2$ by $3$ .

$\sqrt[4]{27000 x^{6}}$

Step 4

Rewrite $27000 x^{6}$ as $x^{4} \cdot (27000 x^{2})$ .

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Step 4.1

Factor out $x^{4}$ .

$\sqrt[4]{27000 (x^{4} x^{2})}$

Step 4.2

Reorder $27000$ and $x^{4}$ .

$\sqrt[4]{x^{4} \cdot 27000 x^{2}}$

Step 4.3

Add parentheses.

$\sqrt[4]{x^{4} \cdot (27000 x^{2})}$

Step 5

Pull terms out from under the radical.

$x \sqrt[4]{27000 x^{2}}$