Simplify -7s(2r)(-4r^8s^2)

$- 7 s (2 r) (- 4 r^{8} s^{2})$

Step 1

Multiply $s$ by $s^{2}$ by adding the exponents.

Move $s^{2}$ .

$- 7 (s^{2} s) (2 r) (- 4 r^{8})$

Multiply $s^{2}$ by $s$ .

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

$- 7 (s^{2} s^{1}) (2 r) (- 4 r^{8})$

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

$- 7 s^{2 + 1} (2 r) (- 4 r^{8})$

Add $2$ and $1$ .

$- 7 s^{3} (2 r) (- 4 r^{8})$

Step 2

Multiply $r$ by $r^{8}$ by adding the exponents.

Move $r^{8}$ .

$- 7 s^{3} (2 (r^{8} r)) \cdot - 4$

Multiply $r^{8}$ by $r$ .

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

$- 7 s^{3} (2 (r^{8} r^{1})) \cdot - 4$

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

$- 7 s^{3} (2 r^{8 + 1}) \cdot - 4$

Add $8$ and $1$ .

$- 7 s^{3} (2 r^{9}) \cdot - 4$

Step 3

Rewrite using the commutative property of multiplication.

$- 7 \cdot 2 s^{3} r^{9} \cdot - 4$

Step 4

Multiply $- 7$ by $2$ .

$- 14 s^{3} r^{9} \cdot - 4$

Step 5

Multiply $- 4$ by $- 14$ .

$56 s^{3} r^{9}$