Simplify (4c^-3)/(-4(d^4c^5)^-4)

$\frac{4 c^{- 3}}{- 4 {(d^{4} c^{5})}^{- 4}}$

Step 1

Reduce the expression by cancelling the common factors.

Move $c^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{4}{- 4 {(d^{4} c^{5})}^{- 4} c^{3}}$

Move ${(d^{4} c^{5})}^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{4 {(d^{4} c^{5})}^{4}}{- 4 c^{3}}$

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

Factor $4$ out of $4 {(d^{4} c^{5})}^{4}$ .

$\frac{4 ({(d^{4} c^{5})}^{4})}{- 4 c^{3}}$

Cancel the common factors.

Factor $4$ out of $- 4 c^{3}$ .

$\frac{4 ({(d^{4} c^{5})}^{4})}{4 (- c^{3})}$

Cancel the common factor.

$\frac{4 {(d^{4} c^{5})}^{4}}{4 (- c^{3})}$

Rewrite the expression.

$\frac{{(d^{4} c^{5})}^{4}}{- c^{3}}$

Step 2

Simplify the numerator.

Apply the product rule to $d^{4} c^{5}$ .

$\frac{{(d^{4})}^{4} {(c^{5})}^{4}}{- c^{3}}$

Multiply the exponents in ${(d^{4})}^{4}$ .

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

$\frac{d^{4 \cdot 4} {(c^{5})}^{4}}{- c^{3}}$

Multiply $4$ by $4$ .

$\frac{d^{16} {(c^{5})}^{4}}{- c^{3}}$

Multiply the exponents in ${(c^{5})}^{4}$ .

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

$\frac{d^{16} c^{5 \cdot 4}}{- c^{3}}$

Multiply $5$ by $4$ .

$\frac{d^{16} c^{20}}{- c^{3}}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $c^{20}$ and $c^{3}$ .

Factor $c^{3}$ out of $d^{16} c^{20}$ .

$\frac{c^{3} (d^{16} c^{17})}{- c^{3}}$

Move the negative one from the denominator of $\frac{d^{16} c^{17}}{- 1}$ .

$- 1 \cdot (d^{16} c^{17})$

Rewrite $- 1 \cdot (d^{16} c^{17})$ as $- (d^{16} c^{17})$ .

$- d^{16} c^{17}$