Simplify (8xy^3*2x^3y^4)/((-7x^3y)^2-x^6y^2)

$\frac{8 x y^{3} \cdot 2 x^{3} y^{4}}{{(- 7 x^{3} y)}^{2} - x^{6} y^{2}}$

Multiply $x$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$\frac{8 (x^{3} x) y^{3} \cdot (2 y^{4})}{{(- 7 x^{3} y)}^{2} - x^{6} y^{2}}$

Multiply $x^{3}$ by $x$ .

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

$\frac{8 (x^{3} x^{1}) y^{3} \cdot (2 y^{4})}{{(- 7 x^{3} y)}^{2} - x^{6} y^{2}}$

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

$\frac{8 x^{3 + 1} y^{3} \cdot (2 y^{4})}{{(- 7 x^{3} y)}^{2} - x^{6} y^{2}}$

Add $3$ and $1$ .

$\frac{8 x^{4} y^{3} \cdot (2 y^{4})}{{(- 7 x^{3} y)}^{2} - x^{6} y^{2}}$

Multiply $y^{3}$ by $y^{4}$ by adding the exponents.

Move $y^{4}$ .

$\frac{8 x^{4} (y^{4} y^{3}) \cdot 2}{{(- 7 x^{3} y)}^{2} - x^{6} y^{2}}$

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

$\frac{8 x^{4} y^{4 + 3} \cdot 2}{{(- 7 x^{3} y)}^{2} - x^{6} y^{2}}$

Add $4$ and $3$ .

$\frac{8 x^{4} y^{7} \cdot 2}{{(- 7 x^{3} y)}^{2} - x^{6} y^{2}}$

Multiply $2$ by $8$ .

$\frac{16 x^{4} y^{7}}{{(- 7 x^{3} y)}^{2} - x^{6} y^{2}}$

Simplify the denominator.

Rewrite $x^{6} y^{2}$ as ${(x^{3} y)}^{2}$ .

$\frac{16 x^{4} y^{7}}{{(- 7 x^{3} y)}^{2} - {(x^{3} y)}^{2}}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = - 7 x^{3} y$ and $b = x^{3} y$ .

$\frac{16 x^{4} y^{7}}{(- 7 x^{3} y + x^{3} y) (- 7 x^{3} y - (x^{3} y))}$

Simplify.

Add $- 7 x^{3} y$ and $x^{3} y$ .

$\frac{16 x^{4} y^{7}}{- 6 x^{3} y (- 7 x^{3} y - (x^{3} y))}$

Subtract $x^{3} y$ from $- 7 x^{3} y$ .

$\frac{16 x^{4} y^{7}}{- 6 x^{3} y \cdot - 8 x^{3} y}$

Combine exponents.

Multiply $- 8$ by $- 6$ .

$\frac{16 x^{4} y^{7}}{48 x^{3} y x^{3} y}$

Multiply $x^{3}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$\frac{16 x^{4} y^{7}}{48 (x^{3} x^{3}) y \cdot y}$

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

$\frac{16 x^{4} y^{7}}{48 x^{3 + 3} y \cdot y}$

Add $3$ and $3$ .

$\frac{16 x^{4} y^{7}}{48 x^{6} y \cdot y}$

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

$\frac{16 x^{4} y^{7}}{48 x^{6} (y^{1} y)}$

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

$\frac{16 x^{4} y^{7}}{48 x^{6} (y^{1} y^{1})}$

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

$\frac{16 x^{4} y^{7}}{48 x^{6} y^{1 + 1}}$

Add $1$ and $1$ .

$\frac{16 x^{4} y^{7}}{48 x^{6} y^{2}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $16$ and $48$ .

Factor $16$ out of $16 x^{4} y^{7}$ .

$\frac{16 (x^{4} y^{7})}{48 x^{6} y^{2}}$

Cancel the common factors.

Factor $16$ out of $48 x^{6} y^{2}$ .

$\frac{16 (x^{4} y^{7})}{16 (3 x^{6} y^{2})}$

Cancel the common factor.

$\frac{16 (x^{4} y^{7})}{16 (3 x^{6} y^{2})}$

Rewrite the expression.

$\frac{x^{4} y^{7}}{3 x^{6} y^{2}}$

Cancel the common factor of $x^{4}$ and $x^{6}$ .

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

$\frac{x^{4} (y^{7})}{3 x^{6} y^{2}}$

Cancel the common factors.

Factor $x^{4}$ out of $3 x^{6} y^{2}$ .

$\frac{x^{4} (y^{7})}{x^{4} (3 x^{2} y^{2})}$

Cancel the common factor.

$\frac{x^{4} y^{7}}{x^{4} (3 x^{2} y^{2})}$

Rewrite the expression.

$\frac{y^{7}}{3 x^{2} y^{2}}$

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

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

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

Cancel the common factors.

Factor $y^{2}$ out of $3 x^{2} y^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify (8xy^3*2x^3y^4)/((-7x^3y)^2-x^6y^2)

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