Simplify 12x^-6y^10*3x^7y

$12 x^{- 6} y^{10} \cdot 3 x^{7} y$

Step 1

Multiply $x^{- 6}$ by $x^{7}$ by adding the exponents.

Move $x^{7}$ .

$12 (x^{7} x^{- 6}) y^{10} \cdot (3 y)$

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

$12 x^{7 - 6} y^{10} \cdot (3 y)$

Subtract $6$ from $7$ .

$12 x^{1} y^{10} \cdot (3 y)$

Step 2

Simplify $12 x^{1} y^{10} \cdot (3 y)$ .

$12 x y^{10} \cdot (3 y)$

Step 3

Multiply $y^{10}$ by $y$ by adding the exponents.

Move $y$ .

$12 x (y \cdot y^{10}) \cdot 3$

Multiply $y$ by $y^{10}$ .

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

$12 x (y^{1} y^{10}) \cdot 3$

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

$12 x y^{1 + 10} \cdot 3$

Add $1$ and $10$ .

$12 x y^{11} \cdot 3$

Step 4

Multiply $3$ by $12$ .

$36 x y^{11}$