Simplify cube root of 27x^12* square root of 64x^6

$\sqrt[3]{27 x^{12}} \cdot \sqrt{64 x^{6}}$

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

$\sqrt[3]{{(3 x^{4})}^{3}} \cdot \sqrt{64 x^{6}}$

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

$3 x^{4} \cdot \sqrt{64 x^{6}}$

Rewrite $64 x^{6}$ as ${(8 x^{3})}^{2}$ .

$3 x^{4} \cdot \sqrt{{(8 x^{3})}^{2}}$

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

$3 x^{4} \cdot (8 x^{3})$

Rewrite using the commutative property of multiplication.

$3 \cdot 8 x^{4} x^{3}$

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

Move $x^{3}$ .

$3 \cdot 8 (x^{3} x^{4})$

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

$3 \cdot 8 x^{3 + 4}$

Add $3$ and $4$ .

$3 \cdot 8 x^{7}$

Multiply $3$ by $8$ .

$24 x^{7}$