Simplify 6a^7b^9*2a^-3b

$6 a^{7} b^{9} \times 2 a^{- 3} b$

Multiply $a^{7}$ by $a^{- 3}$ by adding the exponents.

Move $a^{- 3}$ .

$6 (a^{- 3} a^{7}) b^{9} \cdot (2 b)$

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

$6 a^{- 3 + 7} b^{9} \cdot (2 b)$

Add $- 3$ and $7$ .

$6 a^{4} b^{9} \cdot (2 b)$

Multiply $b^{9}$ by $b$ by adding the exponents.

Move $b$ .

$6 a^{4} (b \cdot b^{9}) \cdot 2$

Multiply $b$ by $b^{9}$ .

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

$6 a^{4} (b^{1} b^{9}) \cdot 2$

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

$6 a^{4} b^{1 + 9} \cdot 2$

Add $1$ and $9$ .

$6 a^{4} b^{10} \cdot 2$

Multiply $2$ by $6$ .

$12 a^{4} b^{10}$