Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

Cancel the common factors.

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Step 1.3.1

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

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

Step 1.3.2

Cancel the common factor.

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

Step 1.3.3

Rewrite the expression.

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

Step 2

Simplify the expression.

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Step 2.1

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

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

Step 2.2

One to any power is one.

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

Step 2.3

Apply the product rule to $- 3 c$ .

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

Step 2.4

Rewrite using the commutative property of multiplication.

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

Step 2.5

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

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

Step 3

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

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

Step 4

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

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

$81$