Simplify ((-2xy)^2*10x^3y^11)/(8x^10y^4)

$\frac{{(- 2 x y)}^{2} \cdot 10 x^{3} y^{11}}{8 x^{10} y^{4}}$

Step 1

Reduce the expression by cancelling the common factors.

Cancel the common factor of $10$ and $8$ .

Factor $2$ out of ${(- 2 x y)}^{2} \cdot (10 x^{3} y^{11})$ .

$\frac{2 ({(- 2 x y)}^{2} \cdot (5 x^{3} y^{11}))}{8 x^{10} y^{4}}$

Cancel the common factors.

Factor $2$ out of $8 x^{10} y^{4}$ .

$\frac{2 ({(- 2 x y)}^{2} \cdot (5 x^{3} y^{11}))}{2 (4 x^{10} y^{4})}$

Cancel the common factor.

$\frac{2 ({(- 2 x y)}^{2} \cdot (5 x^{3} y^{11}))}{2 (4 x^{10} y^{4})}$

Rewrite the expression.

$\frac{{(- 2 x y)}^{2} \cdot (5 x^{3} y^{11})}{4 x^{10} y^{4}}$

Cancel the common factor of $x^{3}$ and $x^{10}$ .

Factor $x^{3}$ out of ${(- 2 x y)}^{2} \cdot (5 x^{3} y^{11})$ .

$\frac{x^{3} ({(- 2 x y)}^{2} \cdot (5 y^{11}))}{4 x^{10} y^{4}}$

Cancel the common factors.

Factor $x^{3}$ out of $4 x^{10} y^{4}$ .

$\frac{x^{3} ({(- 2 x y)}^{2} \cdot (5 y^{11}))}{x^{3} (4 x^{7} y^{4})}$

Cancel the common factor.

$\frac{x^{3} ({(- 2 x y)}^{2} \cdot (5 y^{11}))}{x^{3} (4 x^{7} y^{4})}$

Rewrite the expression.

$\frac{{(- 2 x y)}^{2} \cdot (5 y^{11})}{4 x^{7} y^{4}}$

Cancel the common factor of $y^{11}$ and $y^{4}$ .

Factor $y^{4}$ out of ${(- 2 x y)}^{2} \cdot (5 y^{11})$ .

$\frac{y^{4} ({(- 2 x y)}^{2} \cdot (5 y^{7}))}{4 x^{7} y^{4}}$

Cancel the common factors.

Factor $y^{4}$ out of $4 x^{7} y^{4}$ .

$\frac{y^{4} ({(- 2 x y)}^{2} \cdot (5 y^{7}))}{y^{4} (4 x^{7})}$

Cancel the common factor.

$\frac{y^{4} ({(- 2 x y)}^{2} \cdot (5 y^{7}))}{y^{4} (4 x^{7})}$

Rewrite the expression.

$\frac{{(- 2 x y)}^{2} \cdot (5 y^{7})}{4 x^{7}}$

Step 2

Simplify the numerator.

Apply the product rule to $- 2 x y$ .

$\frac{{(- 2 x)}^{2} y^{2} \cdot 5 y^{7}}{4 x^{7}}$

Multiply $y^{2}$ by $y^{7}$ by adding the exponents.

Move $y^{7}$ .

$\frac{{(- 2 x)}^{2} (y^{7} y^{2}) \cdot 5}{4 x^{7}}$

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

$\frac{{(- 2 x)}^{2} y^{7 + 2} \cdot 5}{4 x^{7}}$

Add $7$ and $2$ .

$\frac{{(- 2 x)}^{2} y^{9} \cdot 5}{4 x^{7}}$

Apply the product rule to $- 2 x$ .

$\frac{{(- 2)}^{2} x^{2} y^{9} \cdot 5}{4 x^{7}}$

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

$\frac{4 x^{2} y^{9} \cdot 5}{4 x^{7}}$

Multiply $5$ by $4$ .

$\frac{20 x^{2} y^{9}}{4 x^{7}}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $20$ and $4$ .

Factor $4$ out of $20 x^{2} y^{9}$ .

$\frac{4 (5 x^{2} y^{9})}{4 x^{7}}$

Cancel the common factors.

Factor $4$ out of $4 x^{7}$ .

$\frac{4 (5 x^{2} y^{9})}{4 (x^{7})}$

Cancel the common factor.

$\frac{4 (5 x^{2} y^{9})}{4 x^{7}}$

Rewrite the expression.

$\frac{5 x^{2} y^{9}}{x^{7}}$

Cancel the common factor of $x^{2}$ and $x^{7}$ .

Factor $x^{2}$ out of $5 x^{2} y^{9}$ .

$\frac{x^{2} (5 y^{9})}{x^{7}}$

Cancel the common factors.

Factor $x^{2}$ out of $x^{7}$ .

$\frac{x^{2} (5 y^{9})}{x^{2} x^{5}}$

Cancel the common factor.

$\frac{x^{2} (5 y^{9})}{x^{2} x^{5}}$

Rewrite the expression.

$\frac{5 y^{9}}{x^{5}}$

Simplify ((-2xy)^2*10x^3y^11)/(8x^10y^4)

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