Algebra Examples

$\sqrt[4]{81 x^{12}} \cdot \sqrt{144 x^{8}}$

Step 1

Rewrite $81 x^{12}$ as ${(3 x^{3})}^{4}$ .

$\sqrt[4]{{(3 x^{3})}^{4}} \cdot \sqrt{144 x^{8}}$

Step 2

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

$3 x^{3} \cdot \sqrt{144 x^{8}}$

Step 3

Rewrite $144 x^{8}$ as ${(12 x^{4})}^{2}$ .

$3 x^{3} \cdot \sqrt{{(12 x^{4})}^{2}}$

Step 4

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

$3 x^{3} \cdot (12 x^{4})$

Step 5

Rewrite using the commutative property of multiplication.

$3 \cdot 12 x^{3} x^{4}$

Step 6

Multiply $x^{3}$ by $x^{4}$ by adding the exponents.

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Step 6.1

Move $x^{4}$ .

$3 \cdot 12 (x^{4} x^{3})$

Step 6.2

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

$3 \cdot 12 x^{4 + 3}$

Step 6.3

Add $4$ and $3$ .

$3 \cdot 12 x^{7}$

Step 7

Multiply $3$ by $12$ .

$36 x^{7}$