Simplify (16 square root of xy)(-2 square root of xy)

$(16 \sqrt{x y}) (- 2 \sqrt{x y})$

Multiply $(16 \sqrt{x y}) (- 2 \sqrt{x y})$ .

Multiply $- 2$ by $16$ .

$- 32 \sqrt{x y} \sqrt{x y}$

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

$- 32 ({\sqrt{x y}}^{1} \sqrt{x y})$

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

$- 32 ({\sqrt{x y}}^{1} {\sqrt{x y}}^{1})$

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

$- 32 {\sqrt{x y}}^{1 + 1}$

Add $1$ and $1$ .

$- 32 {\sqrt{x y}}^{2}$

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

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

$- 32 {({(x y)}^{\frac{1}{2}})}^{2}$

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

$- 32 {(x y)}^{\frac{1}{2} \cdot 2}$

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

$- 32 {(x y)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 32 {(x y)}^{\frac{2}{2}}$

Rewrite the expression.

$- 32 {(x y)}^{1}$

Simplify.

$- 32 (x y)$

$- 32 x y$