Algebra Examples

$\frac{4 {(c^{- 2})}^{4}}{12 c^{- 1}}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Move $c^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{4 {(c^{- 2})}^{4} c}{12}$

Step 1.2

Cancel the common factor of $4$ and $12$ .

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Step 1.2.1

Factor $4$ out of $4 {(c^{- 2})}^{4} c$ .

$\frac{4 ({(c^{- 2})}^{4} c)}{12}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $4$ out of $12$ .

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

Step 1.2.2.2

Cancel the common factor.

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

Step 1.2.2.3

Rewrite the expression.

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

Step 2

Simplify the numerator.

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Step 2.1

Multiply the exponents in ${(c^{- 2})}^{4}$ .

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Step 2.1.1

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

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

Step 2.1.2

Multiply $- 2$ by $4$ .

$\frac{c^{- 8} c}{3}$

Step 2.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{\frac{1}{c^{8}} c}{3}$

Step 3

Simplify terms.

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Step 3.1

Combine $\frac{1}{c^{8}}$ and $c$ .

$\frac{\frac{c}{c^{8}}}{3}$

Step 3.2

Reduce the expression $\frac{c}{c^{8}}$ by cancelling the common factors.

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Step 3.2.1

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

$\frac{\frac{c^{1}}{c^{8}}}{3}$

Step 3.2.2

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

$\frac{\frac{c \cdot 1}{c^{8}}}{3}$

Step 3.2.3

Factor $c$ out of $c^{8}$ .

$\frac{\frac{c \cdot 1}{c \cdot c^{7}}}{3}$

Step 3.2.4

Cancel the common factor.

$\frac{\frac{c \cdot 1}{c \cdot c^{7}}}{3}$

Step 3.2.5

Rewrite the expression.

$\frac{\frac{1}{c^{7}}}{3}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{c^{7}} \cdot \frac{1}{3}$

Step 5

Combine.

$\frac{1 \cdot 1}{c^{7} \cdot 3}$

Step 6

Simplify the expression.

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Step 6.1

Multiply $1$ by $1$ .

$\frac{1}{c^{7} \cdot 3}$

Step 6.2

Move $3$ to the left of $c^{7}$ .

$\frac{1}{3 c^{7}}$