Simplify (6x^-1y)/( square root of 25x^3y^3)

$\frac{6 x^{- 1} y}{\sqrt{25 x^{3} y^{3}}}$

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

$\frac{6 y}{\sqrt{25 x^{3} y^{3}} x}$

Simplify the denominator.

Rewrite $25 x^{3} y^{3}$ as ${(5 x y)}^{2} (x y)$ .

Rewrite $25$ as $5^{2}$ .

$\frac{6 y}{\sqrt{5^{2} x^{3} y^{3}} x}$

Factor out $x^{2}$ .

$\frac{6 y}{\sqrt{5^{2} (x^{2} x) y^{3}} x}$

Factor out $y^{2}$ .

$\frac{6 y}{\sqrt{5^{2} (x^{2} x) (y^{2} y)} x}$

Move $x$ .

$\frac{6 y}{\sqrt{5^{2} (x^{2}) y^{2} x y} x}$

Rewrite $5^{2} (x^{2}) y^{2}$ as ${(5 x y)}^{2}$ .

$\frac{6 y}{\sqrt{{(5 x y)}^{2} x y} x}$

Add parentheses.

$\frac{6 y}{\sqrt{{(5 x y)}^{2} (x y)} x}$

Pull terms out from under the radical.

$\frac{6 y}{5 x y \sqrt{x y} x}$

Combine exponents.

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

$\frac{6 y}{5 (x^{1} x) y \sqrt{x y}}$

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

$\frac{6 y}{5 (x^{1} x^{1}) y \sqrt{x y}}$

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

$\frac{6 y}{5 x^{1 + 1} y \sqrt{x y}}$

Add $1$ and $1$ .

$\frac{6 y}{5 x^{2} y \sqrt{x y}}$

Cancel the common factor of $y$ .

Cancel the common factor.

$\frac{6 y}{5 x^{2} y \sqrt{x y}}$

Rewrite the expression.

$\frac{6}{5 x^{2} \sqrt{x y}}$

Multiply $\frac{6}{5 x^{2} \sqrt{x y}}$ by $\frac{\sqrt{x y}}{\sqrt{x y}}$ .

$\frac{6}{5 x^{2} \sqrt{x y}} \cdot \frac{\sqrt{x y}}{\sqrt{x y}}$

Combine and simplify the denominator.

Multiply $\frac{6}{5 x^{2} \sqrt{x y}}$ by $\frac{\sqrt{x y}}{\sqrt{x y}}$ .

$\frac{6 \sqrt{x y}}{5 x^{2} \sqrt{x y} \sqrt{x y}}$

Move $\sqrt{x y}$ .

$\frac{6 \sqrt{x y}}{5 x^{2} (\sqrt{x y} \sqrt{x y})}$

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

$\frac{6 \sqrt{x y}}{5 x^{2} ({\sqrt{x y}}^{1} \sqrt{x y})}$

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

$\frac{6 \sqrt{x y}}{5 x^{2} ({\sqrt{x y}}^{1} {\sqrt{x y}}^{1})}$

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

$\frac{6 \sqrt{x y}}{5 x^{2} {\sqrt{x y}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{6 \sqrt{x y}}{5 x^{2} {\sqrt{x y}}^{2}}$

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

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

$\frac{6 \sqrt{x y}}{5 x^{2} {({(x y)}^{\frac{1}{2}})}^{2}}$

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

$\frac{6 \sqrt{x y}}{5 x^{2} {(x y)}^{\frac{1}{2} \cdot 2}}$

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

$\frac{6 \sqrt{x y}}{5 x^{2} {(x y)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{6 \sqrt{x y}}{5 x^{2} {(x y)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{6 \sqrt{x y}}{5 x^{2} {(x y)}^{1}}$

Simplify.

$\frac{6 \sqrt{x y}}{5 x^{2} (x y)}$

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

$\frac{6 \sqrt{x y}}{5 (x \cdot x^{2}) y}$

Multiply $x$ by $x^{2}$ .

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

$\frac{6 \sqrt{x y}}{5 (x^{1} x^{2}) y}$

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

$\frac{6 \sqrt{x y}}{5 x^{1 + 2} y}$

Add $1$ and $2$ .

$\frac{6 \sqrt{x y}}{5 x^{3} y}$

Simplify (6x^-1y)/( square root of 25x^3y^3)

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