Simplify (x^3y^-4)(-8xy^5)

$(x^{3} y^{- 4}) (- 8 x y^{5})$

Step 1

Rewrite using the commutative property of multiplication.

$- 8 x^{3} y^{- 4} (x y^{5})$

Step 2

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

Move $x$ .

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

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

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

$- 8 (x^{1} x^{3}) y^{- 4} y^{5}$

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

$- 8 x^{1 + 3} y^{- 4} y^{5}$

Add $1$ and $3$ .

$- 8 x^{4} y^{- 4} y^{5}$

Step 3

Multiply $y^{- 4}$ by $y^{5}$ by adding the exponents.

Move $y^{5}$ .

$- 8 x^{4} (y^{5} y^{- 4})$

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

$- 8 x^{4} y^{5 - 4}$

Subtract $4$ from $5$ .

$- 8 x^{4} y^{1}$

Step 4

Simplify $- 8 x^{4} y^{1}$ .

$- 8 x^{4} y$