Simplify square root of 100x^4* cube root of 27x^12

$\sqrt{100 x^{4}} \cdot \sqrt[3]{27 x^{12}}$

Rewrite $100 x^{4}$ as ${(10 x^{2})}^{2}$ .

$\sqrt{{(10 x^{2})}^{2}} \cdot \sqrt[3]{27 x^{12}}$

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

$10 x^{2} \cdot \sqrt[3]{27 x^{12}}$

Rewrite $27 x^{12}$ as ${(3 x^{4})}^{3}$ .

$10 x^{2} \cdot \sqrt[3]{{(3 x^{4})}^{3}}$

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

$10 x^{2} \cdot (3 x^{4})$

Rewrite using the commutative property of multiplication.

$10 \cdot 3 x^{2} x^{4}$

Multiply $x^{2}$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

$10 \cdot 3 (x^{4} x^{2})$

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

$10 \cdot 3 x^{4 + 2}$

Add $4$ and $2$ .

$10 \cdot 3 x^{6}$

Multiply $10$ by $3$ .

$30 x^{6}$