Simplify (xy^-5)/( square root of 16x^3y^2)

$\frac{x y^{- 5}}{\sqrt{16 x^{3} y^{2}}}$

Move $y^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{x}{\sqrt{16 x^{3} y^{2}} y^{5}}$

Simplify the denominator.

Rewrite $16 x^{3} y^{2}$ as ${(4 x y)}^{2} x$ .

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

$\frac{x}{\sqrt{4^{2} x^{3} y^{2}} y^{5}}$

Factor out $x^{2}$ .

$\frac{x}{\sqrt{4^{2} (x^{2} x) y^{2}} y^{5}}$

Move $x$ .

$\frac{x}{\sqrt{4^{2} x^{2} y^{2} x} y^{5}}$

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

$\frac{x}{\sqrt{{(4 x y)}^{2} x} y^{5}}$

Pull terms out from under the radical.

$\frac{x}{4 x y \sqrt{x} y^{5}}$

Multiply $y$ by $y^{5}$ by adding the exponents.

Move $y^{5}$ .

$\frac{x}{4 x (y^{5} y) \sqrt{x}}$

Multiply $y^{5}$ by $y$ .

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

$\frac{x}{4 x (y^{5} y^{1}) \sqrt{x}}$

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

$\frac{x}{4 x y^{5 + 1} \sqrt{x}}$

Add $5$ and $1$ .

$\frac{x}{4 x y^{6} \sqrt{x}}$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{x}{4 x y^{6} \sqrt{x}}$

Rewrite the expression.

$\frac{1}{4 y^{6} \sqrt{x}}$

Multiply $\frac{1}{4 y^{6} \sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

$\frac{1}{4 y^{6} \sqrt{x}} \cdot \frac{\sqrt{x}}{\sqrt{x}}$

Combine and simplify the denominator.

Multiply $\frac{1}{4 y^{6} \sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

$\frac{\sqrt{x}}{4 y^{6} \sqrt{x} \sqrt{x}}$

Move $\sqrt{x}$ .

$\frac{\sqrt{x}}{4 y^{6} (\sqrt{x} \sqrt{x})}$

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

$\frac{\sqrt{x}}{4 y^{6} ({\sqrt{x}}^{1} \sqrt{x})}$

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

$\frac{\sqrt{x}}{4 y^{6} ({\sqrt{x}}^{1} {\sqrt{x}}^{1})}$

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

$\frac{\sqrt{x}}{4 y^{6} {\sqrt{x}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt{x}}{4 y^{6} {\sqrt{x}}^{2}}$

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

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

$\frac{\sqrt{x}}{4 y^{6} {(x^{\frac{1}{2}})}^{2}}$

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

$\frac{\sqrt{x}}{4 y^{6} x^{\frac{1}{2} \cdot 2}}$

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

$\frac{\sqrt{x}}{4 y^{6} x^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{x}}{4 y^{6} x^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{\sqrt{x}}{4 y^{6} x^{1}}$

Simplify.

$\frac{\sqrt{x}}{4 y^{6} x}$

Simplify (xy^-5)/( square root of 16x^3y^2)

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