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

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

Step 1

Move $d^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(c^{- 3})}^{2} d^{4} d^{2}$

Step 2

Multiply $d^{4}$ by $d^{2}$ by adding the exponents.

Move $d^{2}$ .

${(c^{- 3})}^{2} (d^{2} d^{4})$

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

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

Add $2$ and $4$ .

${(c^{- 3})}^{2} d^{6}$

Step 3

Multiply the exponents in ${(c^{- 3})}^{2}$ .

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

$c^{- 3 \cdot 2} d^{6}$

Multiply $- 3$ by $2$ .

$c^{- 6} d^{6}$

Step 4

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

$\frac{1}{c^{6}} d^{6}$

Step 5

Combine $\frac{1}{c^{6}}$ and $d^{6}$ .

$\frac{d^{6}}{c^{6}}$