Write the Fraction in Simplest Form ((-3c^-1)^4)/(-12c^7)

$\frac{{(- 3 c^{- 1})}^{4}}{- 12 c^{7}}$

Step 1

Simplify the numerator.

Apply the product rule to $- 3 c^{- 1}$ .

$\frac{{(- 3)}^{4} {(c^{- 1})}^{4}}{- 12 c^{7}}$

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

$\frac{81 {(c^{- 1})}^{4}}{- 12 c^{7}}$

Multiply the exponents in ${(c^{- 1})}^{4}$ .

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

$\frac{81 c^{- 1 \cdot 4}}{- 12 c^{7}}$

Multiply $- 1$ by $4$ .

$\frac{81 c^{- 4}}{- 12 c^{7}}$

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

$\frac{81 \frac{1}{c^{4}}}{- 12 c^{7}}$

Step 2

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

$\frac{\frac{81}{c^{4}}}{- 12 c^{7}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{81}{c^{4}} \cdot \frac{1}{- 12 c^{7}}$

Step 4

Combine.

$\frac{81 \cdot 1}{c^{4} (- 12 c^{7})}$

Step 5

Multiply $c^{4}$ by $c^{7}$ by adding the exponents.

Move $c^{7}$ .

$\frac{81 \cdot 1}{c^{7} c^{4} \cdot - 12}$

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

$\frac{81 \cdot 1}{c^{7 + 4} \cdot - 12}$

Add $7$ and $4$ .

$\frac{81 \cdot 1}{c^{11} \cdot - 12}$

Step 6

Multiply $81$ by $1$ .

$\frac{81}{c^{11} \cdot - 12}$

Step 7

Cancel the common factor of $81$ and $- 12$ .

Factor $3$ out of $81$ .

$\frac{3 (27)}{c^{11} \cdot - 12}$

Cancel the common factors.

Factor $3$ out of $c^{11} \cdot - 12$ .

$\frac{3 (27)}{3 (c^{11} \cdot - 4)}$

Cancel the common factor.

$\frac{3 \cdot 27}{3 (c^{11} \cdot - 4)}$

Rewrite the expression.

$\frac{27}{c^{11} \cdot - 4}$

Step 8

Move $- 4$ to the left of $c^{11}$ .

$\frac{27}{- 4 \cdot c^{11}}$

Step 9

Move the negative in front of the fraction.

$- \frac{27}{4 c^{11}}$

Write the Fraction in Simplest Form ((-3c^-1)^4)/(-12c^7)

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