Simplify (-5x^-2y)*(6x^7y^-1)+7x^5

$(- 5 x^{- 2} y) \cdot (6 x^{7} y^{- 1}) + 7 x^{5}$

Step 1

Simplify each term.

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

Move $x^{7}$ .

$- 5 (x^{7} x^{- 2}) y \cdot (6 y^{- 1}) + 7 x^{5}$

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

$- 5 x^{7 - 2} y \cdot (6 y^{- 1}) + 7 x^{5}$

Subtract $2$ from $7$ .

$- 5 x^{5} y \cdot (6 y^{- 1}) + 7 x^{5}$

Multiply $y$ by $y^{- 1}$ by adding the exponents.

Move $y^{- 1}$ .

$- 5 x^{5} (y^{- 1} y) \cdot 6 + 7 x^{5}$

Multiply $y^{- 1}$ by $y$ .

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

$- 5 x^{5} (y^{- 1} y^{1}) \cdot 6 + 7 x^{5}$

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

$- 5 x^{5} y^{- 1 + 1} \cdot 6 + 7 x^{5}$

Add $- 1$ and $1$ .

$- 5 x^{5} y^{0} \cdot 6 + 7 x^{5}$

Simplify $- 5 x^{5} y^{0} \cdot 6$ .

$- 5 x^{5} \cdot 6 + 7 x^{5}$

Multiply $6$ by $- 5$ .

$- 30 x^{5} + 7 x^{5}$

Step 2

Add $- 30 x^{5}$ and $7 x^{5}$ .

$- 23 x^{5}$