Simplify 7x^2 square root of 2x^4*6 square root of 2x^12

$7 x^{2} \sqrt{2 x^{4}} \cdot 6 \sqrt{2 x^{12}}$

Rewrite $2 x^{4}$ as ${(x^{2})}^{2} \cdot 2$ .

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

$7 x^{2} \sqrt{2 {(x^{2})}^{2}} \cdot (6 \sqrt{2 x^{12}})$

Reorder $2$ and ${(x^{2})}^{2}$ .

$7 x^{2} \sqrt{{(x^{2})}^{2} \cdot 2} \cdot (6 \sqrt{2 x^{12}})$

Pull terms out from under the radical.

$7 x^{2} (x^{2} \sqrt{2}) \cdot (6 \sqrt{2 x^{12}})$

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

Move $x^{2}$ .

$7 (x^{2} x^{2}) \sqrt{2} \cdot (6 \sqrt{2 x^{12}})$

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

$7 x^{2 + 2} \sqrt{2} \cdot (6 \sqrt{2 x^{12}})$

Add $2$ and $2$ .

$7 x^{4} \sqrt{2} \cdot (6 \sqrt{2 x^{12}})$

Rewrite $2 x^{12}$ as ${({(x^{3})}^{2})}^{2} \cdot 2$ .

Rewrite $x^{12}$ as ${(x^{6})}^{2}$ .

$7 x^{4} \sqrt{2} \cdot (6 \sqrt{2 {(x^{6})}^{2}})$

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

$7 x^{4} \sqrt{2} \cdot (6 \sqrt{{(x^{6})}^{2} \cdot 2})$

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

$7 x^{4} \sqrt{2} \cdot (6 \sqrt{{({(x^{3})}^{2})}^{2} \cdot 2})$

Pull terms out from under the radical.

$7 x^{4} \sqrt{2} \cdot (6 ({(x^{3})}^{2} \sqrt{2}))$

Multiply the exponents in ${(x^{3})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$7 x^{4} \sqrt{2} \cdot (6 (x^{3 \cdot 2} \sqrt{2}))$

Multiply $3$ by $2$ .

$7 x^{4} \sqrt{2} \cdot (6 (x^{6} \sqrt{2}))$

Multiply $x^{4}$ by $x^{6}$ by adding the exponents.

Move $x^{6}$ .

$7 (x^{6} x^{4}) \sqrt{2} \cdot (6 (\sqrt{2}))$

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

$7 x^{6 + 4} \sqrt{2} \cdot (6 (\sqrt{2}))$

Add $6$ and $4$ .

$7 x^{10} \sqrt{2} \cdot (6 (\sqrt{2}))$

Multiply $7 x^{10} \sqrt{2} (6 \sqrt{2})$ .

Multiply $6$ by $7$ .

$42 x^{10} \sqrt{2} \sqrt{2}$

Raise $\sqrt{2}$ to the power of $1$ .

$42 x^{10} ({\sqrt{2}}^{1} \sqrt{2})$

Raise $\sqrt{2}$ to the power of $1$ .

$42 x^{10} ({\sqrt{2}}^{1} {\sqrt{2}}^{1})$

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

$42 x^{10} {\sqrt{2}}^{1 + 1}$

Add $1$ and $1$ .

$42 x^{10} {\sqrt{2}}^{2}$

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$42 x^{10} {(2^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$42 x^{10} \cdot 2^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$42 x^{10} \cdot 2^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$42 x^{10} \cdot 2^{\frac{2}{2}}$

Rewrite the expression.

$42 x^{10} \cdot 2^{1}$

Evaluate the exponent.

$42 x^{10} \cdot 2$

Multiply $2$ by $42$ .

$84 x^{10}$

Simplify 7x^2 square root of 2x^4*6 square root of 2x^12

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