Simplify (2d^7)/(-4d^9d^5)

$\frac{2 d^{7}}{- 4 d^{9} d^{5}}$

Step 1

Multiply $d^{9}$ by $d^{5}$ by adding the exponents.

Move $d^{5}$ .

$\frac{2 d^{7}}{- 4 (d^{5} d^{9})}$

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

$\frac{2 d^{7}}{- 4 d^{5 + 9}}$

Add $5$ and $9$ .

$\frac{2 d^{7}}{- 4 d^{14}}$

Step 2

Cancel the common factor of $2$ and $- 4$ .

Factor $2$ out of $2 d^{7}$ .

$\frac{2 (d^{7})}{- 4 d^{14}}$

Cancel the common factors.

Factor $2$ out of $- 4 d^{14}$ .

$\frac{2 (d^{7})}{2 (- 2 d^{14})}$

Cancel the common factor.

$\frac{2 d^{7}}{2 (- 2 d^{14})}$

Rewrite the expression.

$\frac{d^{7}}{- 2 d^{14}}$

Step 3

Cancel the common factor of $d^{7}$ and $d^{14}$ .

Multiply by $1$ .

$\frac{d^{7} \cdot 1}{- 2 d^{14}}$

Cancel the common factors.

Factor $d^{7}$ out of $- 2 d^{14}$ .

$\frac{d^{7} \cdot 1}{d^{7} (- 2 d^{7})}$

Cancel the common factor.

$\frac{d^{7} \cdot 1}{d^{7} (- 2 d^{7})}$

Rewrite the expression.

$\frac{1}{- 2 d^{7}}$

Step 4

Move the negative in front of the fraction.

$- \frac{1}{2 d^{7}}$