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

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

Step 1

Multiply $c^{- 3}$ by $c^{4}$ by adding the exponents.

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

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

Add $- 3$ and $4$ .

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

Step 2

Simplify $c^{1}$ .

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

Step 3

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

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

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Change the sign of the exponent by rewriting the base as its reciprocal.

$c^{2}$