Simplify (2x^3y^7*4x^5y^-5)/(3x^-4y^2)

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

Multiply $x^{3}$ by $x^{5}$ by adding the exponents.

Move $x^{5}$ .

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

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

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

Add $5$ and $3$ .

$\frac{2 x^{8} y^{7} \cdot (4 y^{- 5})}{3 x^{- 4} y^{2}}$

Multiply $y^{7}$ by $y^{- 5}$ by adding the exponents.

Move $y^{- 5}$ .

$\frac{2 x^{8} (y^{- 5} y^{7}) \cdot 4}{3 x^{- 4} y^{2}}$

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

$\frac{2 x^{8} y^{- 5 + 7} \cdot 4}{3 x^{- 4} y^{2}}$

Add $- 5$ and $7$ .

$\frac{2 x^{8} y^{2} \cdot 4}{3 x^{- 4} y^{2}}$

Move $x^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{2 x^{8} y^{2} \cdot 4 x^{4}}{3 y^{2}}$

Multiply $x^{8}$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

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

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

$\frac{2 x^{4 + 8} y^{2} \cdot 4}{3 y^{2}}$

Add $4$ and $8$ .

$\frac{2 x^{12} y^{2} \cdot 4}{3 y^{2}}$

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

Cancel the common factor.

$\frac{2 x^{12} y^{2} \cdot 4}{3 y^{2}}$

Rewrite the expression.

$\frac{2 x^{12} \cdot 4}{3}$

Multiply $4$ by $2$ .

$\frac{8 x^{12}}{3}$