Simplify (c/(c^2))^4*(-3c)^4

${(\frac{c}{c^{2}})}^{4} \cdot {(- 3 c)}^{4}$

Cancel the common factor of $c$ and $c^{2}$ .

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

${(\frac{c^{1}}{c^{2}})}^{4} \cdot {(- 3 c)}^{4}$

Factor $c$ out of $c^{1}$ .

${(\frac{c \cdot 1}{c^{2}})}^{4} \cdot {(- 3 c)}^{4}$

Cancel the common factors.

Factor $c$ out of $c^{2}$ .

${(\frac{c \cdot 1}{c \cdot c})}^{4} \cdot {(- 3 c)}^{4}$

Cancel the common factor.

${(\frac{c \cdot 1}{c \cdot c})}^{4} \cdot {(- 3 c)}^{4}$

Rewrite the expression.

${(\frac{1}{c})}^{4} \cdot {(- 3 c)}^{4}$

Simplify the expression.

Apply the product rule to $\frac{1}{c}$ .

$\frac{1^{4}}{c^{4}} \cdot {(- 3 c)}^{4}$

One to any power is one.

$\frac{1}{c^{4}} \cdot {(- 3 c)}^{4}$

Apply the product rule to $- 3 c$ .

$\frac{1}{c^{4}} \cdot ({(- 3)}^{4} c^{4})$

Rewrite using the commutative property of multiplication.

${(- 3)}^{4} \frac{1}{c^{4}} c^{4}$

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

$81 \frac{1}{c^{4}} c^{4}$

Combine $81$ and $\frac{1}{c^{4}}$ .

$\frac{81}{c^{4}} c^{4}$

Cancel the common factor of $c^{4}$ .

Cancel the common factor.

$\frac{81}{c^{4}} c^{4}$

Rewrite the expression.

$81$