Algebra Examples

$\sqrt{36 x^{2}} \cdot \sqrt[4]{81 x^{8}}$

Step 1

Rewrite $36 x^{2}$ as ${(6 x)}^{2}$ .

$\sqrt{{(6 x)}^{2}} \cdot \sqrt[4]{81 x^{8}}$

Step 2

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

$6 x \cdot \sqrt[4]{81 x^{8}}$

Step 3

Rewrite $81 x^{8}$ as ${(3 x^{2})}^{4}$ .

$6 x \cdot \sqrt[4]{{(3 x^{2})}^{4}}$

Step 4

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

$6 x \cdot (3 x^{2})$

Step 5

Rewrite using the commutative property of multiplication.

$6 \cdot 3 x \cdot x^{2}$

Step 6

Multiply $x$ by $x^{2}$ by adding the exponents.

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Step 6.1

Move $x^{2}$ .

$6 \cdot 3 (x^{2} x)$

Step 6.2

Multiply $x^{2}$ by $x$ .

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Step 6.2.1

Raise $x$ to the power of $1$ .

$6 \cdot 3 (x^{2} x^{1})$

Step 6.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$6 \cdot 3 x^{2 + 1}$

Step 6.3

Add $2$ and $1$ .

$6 \cdot 3 x^{3}$

Step 7

Multiply $6$ by $3$ .

$18 x^{3}$