Simplify -5 square root of 2m^6*2 square root of 32m^2

$- 5 \sqrt{2 m^{6}} \cdot 2 \sqrt{32 m^{2}}$

Rewrite $2 m^{6}$ as ${(m^{3})}^{2} \cdot 2$ .

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

$- 5 \sqrt{2 {(m^{3})}^{2}} \cdot (2 \sqrt{32 m^{2}})$

Reorder $2$ and ${(m^{3})}^{2}$ .

$- 5 \sqrt{{(m^{3})}^{2} \cdot 2} \cdot (2 \sqrt{32 m^{2}})$

Pull terms out from under the radical.

$- 5 (m^{3} \sqrt{2}) \cdot (2 \sqrt{32 m^{2}})$

Rewrite $32 m^{2}$ as ${(4 m)}^{2} \cdot 2$ .

Factor $16$ out of $32$ .

$- 5 m^{3} \sqrt{2} \cdot (2 \sqrt{16 (2) m^{2}})$

Rewrite $16$ as $4^{2}$ .

$- 5 m^{3} \sqrt{2} \cdot (2 \sqrt{4^{2} \cdot 2 m^{2}})$

Move $2$ .

$- 5 m^{3} \sqrt{2} \cdot (2 \sqrt{4^{2} m^{2} \cdot 2})$

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

$- 5 m^{3} \sqrt{2} \cdot (2 \sqrt{{(4 m)}^{2} \cdot 2})$

Pull terms out from under the radical.

$- 5 m^{3} \sqrt{2} \cdot (2 (4 m \sqrt{2}))$

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

Move $m$ .

$- 5 (m \cdot m^{3}) \sqrt{2} \cdot (2 (4 \sqrt{2}))$

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

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

$- 5 (m^{1} m^{3}) \sqrt{2} \cdot (2 (4 \sqrt{2}))$

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

$- 5 m^{1 + 3} \sqrt{2} \cdot (2 (4 \sqrt{2}))$

Add $1$ and $3$ .

$- 5 m^{4} \sqrt{2} \cdot (2 (4 \sqrt{2}))$

Multiply $4$ by $2$ .

$- 5 m^{4} \sqrt{2} \cdot (8 \sqrt{2})$

Multiply $- 5 m^{4} \sqrt{2} (8 \sqrt{2})$ .

Multiply $8$ by $- 5$ .

$- 40 m^{4} \sqrt{2} \sqrt{2}$

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

$- 40 m^{4} ({\sqrt{2}}^{1} \sqrt{2})$

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

$- 40 m^{4} ({\sqrt{2}}^{1} {\sqrt{2}}^{1})$

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

$- 40 m^{4} {\sqrt{2}}^{1 + 1}$

Add $1$ and $1$ .

$- 40 m^{4} {\sqrt{2}}^{2}$

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

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

$- 40 m^{4} {(2^{\frac{1}{2}})}^{2}$

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

$- 40 m^{4} \cdot 2^{\frac{1}{2} \cdot 2}$

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

$- 40 m^{4} \cdot 2^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 40 m^{4} \cdot 2^{\frac{2}{2}}$

Rewrite the expression.

$- 40 m^{4} \cdot 2^{1}$

Evaluate the exponent.

$- 40 m^{4} \cdot 2$

Multiply $2$ by $- 40$ .

$- 80 m^{4}$

Simplify -5 square root of 2m^6*2 square root of 32m^2

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