Simplify square root of 591x^15y^3* square root of 591x^15y^3

$\sqrt{591 x^{15} y^{3}} \cdot \sqrt{591 x^{15} y^{3}}$

Step 1

Rewrite $591 x^{15} y^{3}$ as ${(x^{7} y)}^{2} \cdot (591 x y)$ .

Factor out $x^{14}$ .

$\sqrt{591 (x^{14} x) y^{3}} \cdot \sqrt{591 x^{15} y^{3}}$

Rewrite $x^{14}$ as ${(x^{7})}^{2}$ .

$\sqrt{591 ({(x^{7})}^{2} x) y^{3}} \cdot \sqrt{591 x^{15} y^{3}}$

Factor out $y^{2}$ .

$\sqrt{591 ({(x^{7})}^{2} x) (y^{2} y)} \cdot \sqrt{591 x^{15} y^{3}}$

Move $x$ .

$\sqrt{591 {(x^{7})}^{2} y^{2} x y} \cdot \sqrt{591 x^{15} y^{3}}$

Move $591$ .

$\sqrt{{(x^{7})}^{2} y^{2} \cdot 591 x y} \cdot \sqrt{591 x^{15} y^{3}}$

Rewrite $({(x^{7})}^{2}) y^{2}$ as ${(x^{7} y)}^{2}$ .

$\sqrt{{(x^{7} y)}^{2} \cdot 591 x y} \cdot \sqrt{591 x^{15} y^{3}}$

Add parentheses.

$\sqrt{{(x^{7} y)}^{2} \cdot 591 (x y)} \cdot \sqrt{591 x^{15} y^{3}}$

Add parentheses.

$\sqrt{{(x^{7} y)}^{2} \cdot (591 x y)} \cdot \sqrt{591 x^{15} y^{3}}$

Step 2

Pull terms out from under the radical.

$x^{7} y \sqrt{591 x y} \cdot \sqrt{591 x^{15} y^{3}}$

Step 3

Rewrite $591 x^{15} y^{3}$ as ${(x^{7} y)}^{2} \cdot (591 x y)$ .

Factor out $x^{14}$ .

$x^{7} y \sqrt{591 x y} \cdot \sqrt{591 (x^{14} x) y^{3}}$

Rewrite $x^{14}$ as ${(x^{7})}^{2}$ .

$x^{7} y \sqrt{591 x y} \cdot \sqrt{591 ({(x^{7})}^{2} x) y^{3}}$

Factor out $y^{2}$ .

$x^{7} y \sqrt{591 x y} \cdot \sqrt{591 ({(x^{7})}^{2} x) (y^{2} y)}$

Move $x$ .

$x^{7} y \sqrt{591 x y} \cdot \sqrt{591 {(x^{7})}^{2} y^{2} x y}$

Move $591$ .

$x^{7} y \sqrt{591 x y} \cdot \sqrt{{(x^{7})}^{2} y^{2} \cdot 591 x y}$

Rewrite $({(x^{7})}^{2}) y^{2}$ as ${(x^{7} y)}^{2}$ .

$x^{7} y \sqrt{591 x y} \cdot \sqrt{{(x^{7} y)}^{2} \cdot 591 x y}$

Add parentheses.

$x^{7} y \sqrt{591 x y} \cdot \sqrt{{(x^{7} y)}^{2} \cdot 591 (x y)}$

Add parentheses.

$x^{7} y \sqrt{591 x y} \cdot \sqrt{{(x^{7} y)}^{2} \cdot (591 x y)}$

Step 4

Pull terms out from under the radical.

$x^{7} y \sqrt{591 x y} \cdot (x^{7} y \sqrt{591 x y})$

Step 5

Multiply $x^{7}$ by $x^{7}$ by adding the exponents.

Move $x^{7}$ .

$x^{7} x^{7} y \sqrt{591 x y} \cdot (y \sqrt{591 x y})$

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

$x^{7 + 7} y \sqrt{591 x y} \cdot (y \sqrt{591 x y})$

Add $7$ and $7$ .

$x^{14} y \sqrt{591 x y} \cdot (y \sqrt{591 x y})$

Step 6

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$x^{14} (y \cdot y) \sqrt{591 x y} \cdot \sqrt{591 x y}$

Multiply $y$ by $y$ .

$x^{14} y^{2} \sqrt{591 x y} \cdot \sqrt{591 x y}$

Step 7

Multiply $x^{14} y^{2} \sqrt{591 x y} \sqrt{591 x y}$ .

Raise $\sqrt{591 x y}$ to the power of $1$ .

$x^{14} y^{2} ({\sqrt{591 x y}}^{1} \sqrt{591 x y})$

Raise $\sqrt{591 x y}$ to the power of $1$ .

$x^{14} y^{2} ({\sqrt{591 x y}}^{1} {\sqrt{591 x y}}^{1})$

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

$x^{14} y^{2} {\sqrt{591 x y}}^{1 + 1}$

Add $1$ and $1$ .

$x^{14} y^{2} {\sqrt{591 x y}}^{2}$

Step 8

Rewrite ${\sqrt{591 x y}}^{2}$ as $591 x y$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{591 x y}$ as ${(591 x y)}^{\frac{1}{2}}$ .

$x^{14} y^{2} {({(591 x y)}^{\frac{1}{2}})}^{2}$

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

$x^{14} y^{2} {(591 x y)}^{\frac{1}{2} \cdot 2}$

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

$x^{14} y^{2} {(591 x y)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{14} y^{2} {(591 x y)}^{\frac{2}{2}}$

Rewrite the expression.

$x^{14} y^{2} {(591 x y)}^{1}$

Simplify.

$x^{14} y^{2} (591 x y)$

Step 9

Rewrite using the commutative property of multiplication.

$591 x^{14} y^{2} (x y)$

Step 10

Multiply $x^{14}$ by $x$ by adding the exponents.

Move $x$ .

$591 (x \cdot x^{14}) y^{2} y$

Multiply $x$ by $x^{14}$ .

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

$591 (x^{1} x^{14}) y^{2} y$

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

$591 x^{1 + 14} y^{2} y$

Add $1$ and $14$ .

$591 x^{15} y^{2} y$

Step 11

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

Move $y$ .

$591 x^{15} (y \cdot y^{2})$

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

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

$591 x^{15} (y^{1} y^{2})$

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

$591 x^{15} y^{1 + 2}$

Add $1$ and $2$ .

$591 x^{15} y^{3}$

Simplify square root of 591x^15y^3* square root of 591x^15y^3

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