Simplify (8c^9d^5)(4c^2d^3)-(19c^10d)(cd^7)

$(8 c^{9} d^{5}) (4 c^{2} d^{3}) - (19 c^{10} d) (c d^{7})$

Step 1

Simplify each term.

Multiply $c^{9}$ by $c^{2}$ by adding the exponents.

Move $c^{2}$ .

$8 (c^{2} c^{9}) d^{5} (4 d^{3}) - 19 c^{10} d (c d^{7})$

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

$8 c^{2 + 9} d^{5} (4 d^{3}) - 19 c^{10} d (c d^{7})$

Add $2$ and $9$ .

$8 c^{11} d^{5} (4 d^{3}) - 19 c^{10} d (c d^{7})$

Multiply $d^{5}$ by $d^{3}$ by adding the exponents.

Move $d^{3}$ .

$8 c^{11} (d^{3} d^{5}) \cdot 4 - 19 c^{10} d (c d^{7})$

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

$8 c^{11} d^{3 + 5} \cdot 4 - 19 c^{10} d (c d^{7})$

Add $3$ and $5$ .

$8 c^{11} d^{8} \cdot 4 - 19 c^{10} d (c d^{7})$

Multiply $4$ by $8$ .

$32 c^{11} d^{8} - 19 c^{10} d (c d^{7})$

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

Move $c$ .

$32 c^{11} d^{8} - 19 (c \cdot c^{10}) d \cdot d^{7}$

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

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

$32 c^{11} d^{8} - 19 (c^{1} c^{10}) d \cdot d^{7}$

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

$32 c^{11} d^{8} - 19 c^{1 + 10} d \cdot d^{7}$

Add $1$ and $10$ .

$32 c^{11} d^{8} - 19 c^{11} d \cdot d^{7}$

Multiply $d$ by $d^{7}$ by adding the exponents.

Move $d^{7}$ .

$32 c^{11} d^{8} - 19 c^{11} (d^{7} d)$

Multiply $d^{7}$ by $d$ .

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

$32 c^{11} d^{8} - 19 c^{11} (d^{7} d^{1})$

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

$32 c^{11} d^{8} - 19 c^{11} d^{7 + 1}$

Add $7$ and $1$ .

$32 c^{11} d^{8} - 19 c^{11} d^{8}$

Step 2

Subtract $19 c^{11} d^{8}$ from $32 c^{11} d^{8}$ .

$13 c^{11} d^{8}$