Simplify (5z^4)(4z^3)(2z)

$(5 z^{4}) (4 z^{3}) (2 z)$

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

Move $z^{3}$ .

$5 (z^{3} z^{4}) \cdot 4 (2 z)$

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

$5 z^{3 + 4} \cdot 4 (2 z)$

Add $3$ and $4$ .

$5 z^{7} \cdot 4 (2 z)$

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

Move $z$ .

$5 (z \cdot z^{7}) \cdot 4 \cdot 2$

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

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

$5 (z^{1} z^{7}) \cdot 4 \cdot 2$

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

$5 z^{1 + 7} \cdot 4 \cdot 2$

Add $1$ and $7$ .

$5 z^{8} \cdot 4 \cdot 2$

Multiply $4$ by $5$ .

$20 z^{8} \cdot 2$

Multiply $2$ by $20$ .

$40 z^{8}$