Simplify (4c^4)(ac^3)(3a^5c)

$(4 c^{4}) (a c^{3}) (3 a^{5} c)$

Multiply $c^{4}$ by $c^{3}$ by adding the exponents.

Move $c^{3}$ .

$4 (c^{3} c^{4}) a (3 a^{5} c)$

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

$4 c^{3 + 4} a (3 a^{5} c)$

Add $3$ and $4$ .

$4 c^{7} a (3 a^{5} c)$

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

Move $c$ .

$4 (c \cdot c^{7}) a (3 a^{5})$

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

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

$4 (c^{1} c^{7}) a (3 a^{5})$

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

$4 c^{1 + 7} a (3 a^{5})$

Add $1$ and $7$ .

$4 c^{8} a (3 a^{5})$

Multiply $a$ by $a^{5}$ by adding the exponents.

Move $a^{5}$ .

$4 c^{8} (a^{5} a) \cdot 3$

Multiply $a^{5}$ by $a$ .

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

$4 c^{8} (a^{5} a^{1}) \cdot 3$

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

$4 c^{8} a^{5 + 1} \cdot 3$

Add $5$ and $1$ .

$4 c^{8} a^{6} \cdot 3$

Multiply $3$ by $4$ .

$12 c^{8} a^{6}$