Simplify ((16 square root of x)^2)/(y^-1)

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

Simplify the expression.

Move $y^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Apply the product rule to $16 \sqrt{x}$ .

$16^{2} {\sqrt{x}}^{2} y$

Raise $16$ to the power of $2$ .

$256 {\sqrt{x}}^{2} y$

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

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

$256 {(x^{\frac{1}{2}})}^{2} y$

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

$256 x^{\frac{1}{2} \cdot 2} y$

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

$256 x^{\frac{2}{2}} y$

Cancel the common factor of $2$ .

Cancel the common factor.

$256 x^{\frac{2}{2}} y$

Rewrite the expression.

$256 x^{1} y$

Simplify.

$256 x y$