Simplify (3x square root of 2x)(4x square root of 3x^3)

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

Step 1

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

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

Step 2

Rewrite $3 x^{3}$ as $x^{2} \cdot (3 x)$ .

Factor out $x^{2}$ .

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

Reorder $3$ and $x^{2}$ .

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

Add parentheses.

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

Step 3

Pull terms out from under the radical.

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

Step 4

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

Move $x$ .

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

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

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

$3 (x^{1} x^{2}) \sqrt{2 x} (4 (\sqrt{3 x}))$

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

$3 x^{1 + 2} \sqrt{2 x} (4 (\sqrt{3 x}))$

Add $1$ and $2$ .

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

Step 5

Multiply $3 x^{3} \sqrt{2 x} (4 \sqrt{3 x})$ .

Multiply $4$ by $3$ .

$12 x^{3} \sqrt{2 x} \sqrt{3 x}$

Combine using the product rule for radicals.

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

Multiply $2$ by $3$ .

$12 x^{3} \sqrt{6 x \cdot x}$

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

$12 x^{3} \sqrt{6 (x^{1} x)}$

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

$12 x^{3} \sqrt{6 (x^{1} x^{1})}$

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

$12 x^{3} \sqrt{6 x^{1 + 1}}$

Add $1$ and $1$ .

$12 x^{3} \sqrt{6 x^{2}}$

Step 6

Reorder $6$ and $x^{2}$ .

$12 x^{3} \sqrt{x^{2} \cdot 6}$

Step 7

Pull terms out from under the radical.

$12 x^{3} (x \sqrt{6})$

Step 8

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

Move $x$ .

$12 (x \cdot x^{3}) \sqrt{6}$

Multiply $x$ by $x^{3}$ .

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

$12 (x^{1} x^{3}) \sqrt{6}$

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

$12 x^{1 + 3} \sqrt{6}$

Add $1$ and $3$ .

$12 x^{4} \sqrt{6}$

Simplify (3x square root of 2x)(4x square root of 3x^3)

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