Simplify ((4xy^6)(3x^5))/(2x^-2y^10)

$\frac{(4 x y^{6}) (3 x^{5})}{2 x^{- 2} y^{10}}$

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

Move $x^{5}$ .

$\frac{4 (x^{5} x) y^{6} \cdot 3}{2 x^{- 2} y^{10}}$

Multiply $x^{5}$ by $x$ .

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

$\frac{4 (x^{5} x^{1}) y^{6} \cdot 3}{2 x^{- 2} y^{10}}$

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

$\frac{4 x^{5 + 1} y^{6} \cdot 3}{2 x^{- 2} y^{10}}$

Add $5$ and $1$ .

$\frac{4 x^{6} y^{6} \cdot 3}{2 x^{- 2} y^{10}}$

Move $x^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{4 x^{6} y^{6} \cdot 3 x^{2}}{2 y^{10}}$

Multiply $x^{6}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$\frac{4 (x^{2} x^{6}) y^{6} \cdot 3}{2 y^{10}}$

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

$\frac{4 x^{2 + 6} y^{6} \cdot 3}{2 y^{10}}$

Add $2$ and $6$ .

$\frac{4 x^{8} y^{6} \cdot 3}{2 y^{10}}$

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4 x^{8} y^{6} \cdot 3$ .

$\frac{2 (2 x^{8} y^{6} \cdot 3)}{2 y^{10}}$

Cancel the common factors.

Factor $2$ out of $2 y^{10}$ .

$\frac{2 (2 x^{8} y^{6} \cdot 3)}{2 (y^{10})}$

Cancel the common factor.

$\frac{2 (2 x^{8} y^{6} \cdot 3)}{2 y^{10}}$

Rewrite the expression.

$\frac{2 x^{8} y^{6} \cdot 3}{y^{10}}$

Cancel the common factor of $y^{6}$ and $y^{10}$ .

Factor $y^{6}$ out of $2 x^{8} y^{6} \cdot 3$ .

$\frac{y^{6} (2 x^{8} \cdot 3)}{y^{10}}$

Cancel the common factors.

Factor $y^{6}$ out of $y^{10}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $3$ by $2$ .

$\frac{6 x^{8}}{y^{4}}$