Simplify (-8 square root of 2)(1/2* square root of 32)

$(- 8 \sqrt{2}) (\frac{1}{2} \cdot \sqrt{32})$

Step 1

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

Factor $16$ out of $32$ .

$- 8 \sqrt{2} (\frac{1}{2} \cdot \sqrt{16 (2)})$

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

$- 8 \sqrt{2} (\frac{1}{2} \cdot \sqrt{4^{2} \cdot 2})$

Step 2

Pull terms out from under the radical.

$- 8 \sqrt{2} (\frac{1}{2} \cdot (4 \sqrt{2}))$

Step 3

Cancel the common factor of $2$ .

Factor $2$ out of $4 \sqrt{2}$ .

$- 8 \sqrt{2} (\frac{1}{2} \cdot (2 (2 \sqrt{2})))$

Cancel the common factor.

$- 8 \sqrt{2} (\frac{1}{2} \cdot (2 (2 \sqrt{2})))$

Rewrite the expression.

$- 8 \sqrt{2} (2 \sqrt{2})$

Step 4

Multiply $- 8 \sqrt{2} (2 \sqrt{2})$ .

Multiply $2$ by $- 8$ .

$- 16 \sqrt{2} \sqrt{2}$

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

$- 16 ({\sqrt{2}}^{1} \sqrt{2})$

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

$- 16 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})$

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

$- 16 {\sqrt{2}}^{1 + 1}$

Add $1$ and $1$ .

$- 16 {\sqrt{2}}^{2}$

Step 5

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

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

$- 16 {(2^{\frac{1}{2}})}^{2}$

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

$- 16 \cdot 2^{\frac{1}{2} \cdot 2}$

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

$- 16 \cdot 2^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 16 \cdot 2^{\frac{2}{2}}$

Rewrite the expression.

$- 16 \cdot 2^{1}$

Evaluate the exponent.

$- 16 \cdot 2$

Step 6

Multiply $- 16$ by $2$ .

$- 32$

Simplify (-8 square root of 2)(1/2* square root of 32)

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