Simplify (-3b^6)^4*b

${(- 3 b^{6})}^{4} \cdot b$

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

${(- 3)}^{4} {(b^{6})}^{4} \cdot b$

Raise $- 3$ to the power of $4$ .

$81 {(b^{6})}^{4} \cdot b$

Multiply the exponents in ${(b^{6})}^{4}$ .

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

$81 b^{6 \cdot 4} \cdot b$

Multiply $6$ by $4$ .

$81 b^{24} \cdot b$

Multiply $b^{24}$ by $b$ by adding the exponents.

Move $b$ .

$81 (b \cdot b^{24})$

Multiply $b$ by $b^{24}$ .

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

$81 (b^{1} b^{24})$

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

$81 b^{1 + 24}$

Add $1$ and $24$ .

$81 b^{25}$