Simplify (3y^6)^2(x^5y^2z)

${(3 y^{6})}^{2} (x^{5} y^{2} z)$

Apply the product rule to $3 y^{6}$ .

$3^{2} {(y^{6})}^{2} (x^{5} y^{2} z)$

Raise $3$ to the power of $2$ .

$9 {(y^{6})}^{2} (x^{5} y^{2} z)$

Multiply the exponents in ${(y^{6})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$9 y^{6 \cdot 2} (x^{5} y^{2} z)$

Multiply $6$ by $2$ .

$9 y^{12} (x^{5} y^{2} z)$

Multiply $y^{12}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$9 (y^{2} y^{12}) (x^{5} z)$

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

$9 y^{2 + 12} (x^{5} z)$

Add $2$ and $12$ .

$9 y^{14} (x^{5} z)$

$9 y^{14} x^{5} z$