Simplify (2a^2b^4z)(6a^3b^2z^5)

$(2 a^{2} b^{4} z) (6 a^{3} b^{2} z^{5})$

Multiply $a^{2}$ by $a^{3}$ by adding the exponents.

Move $a^{3}$ .

$2 (a^{3} a^{2}) b^{4} z (6 b^{2} z^{5})$

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

$2 a^{3 + 2} b^{4} z (6 b^{2} z^{5})$

Add $3$ and $2$ .

$2 a^{5} b^{4} z (6 b^{2} z^{5})$

Multiply $b^{4}$ by $b^{2}$ by adding the exponents.

Move $b^{2}$ .

$2 a^{5} (b^{2} b^{4}) z (6 z^{5})$

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

$2 a^{5} b^{2 + 4} z (6 z^{5})$

Add $2$ and $4$ .

$2 a^{5} b^{6} z (6 z^{5})$

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

Move $z^{5}$ .

$2 a^{5} b^{6} (z^{5} z) \cdot 6$

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

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

$2 a^{5} b^{6} (z^{5} z^{1}) \cdot 6$

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

$2 a^{5} b^{6} z^{5 + 1} \cdot 6$

Add $5$ and $1$ .

$2 a^{5} b^{6} z^{6} \cdot 6$

Multiply $6$ by $2$ .

$12 a^{5} b^{6} z^{6}$