Write the Fraction in Simplest Form ((-4q^3)^2)/(-2q^9)

$\frac{{(- 4 q^{3})}^{2}}{- 2 q^{9}}$

Step 1

Simplify the numerator.

Apply the product rule to $- 4 q^{3}$ .

$\frac{{(- 4)}^{2} {(q^{3})}^{2}}{- 2 q^{9}}$

Raise $- 4$ to the power of $2$ .

$\frac{16 {(q^{3})}^{2}}{- 2 q^{9}}$

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

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

$\frac{16 q^{3 \cdot 2}}{- 2 q^{9}}$

Multiply $3$ by $2$ .

$\frac{16 q^{6}}{- 2 q^{9}}$

Step 2

Cancel the common factor of $16$ and $- 2$ .

Factor $2$ out of $16 q^{6}$ .

$\frac{2 (8 q^{6})}{- 2 q^{9}}$

Cancel the common factors.

Factor $2$ out of $- 2 q^{9}$ .

$\frac{2 (8 q^{6})}{2 (- q^{9})}$

Cancel the common factor.

$\frac{2 (8 q^{6})}{2 (- q^{9})}$

Rewrite the expression.

$\frac{8 q^{6}}{- q^{9}}$

Step 3

Cancel the common factor of $q^{6}$ and $q^{9}$ .

Factor $q^{6}$ out of $8 q^{6}$ .

$\frac{q^{6} \cdot 8}{- q^{9}}$

Cancel the common factors.

Factor $q^{6}$ out of $- q^{9}$ .

$\frac{q^{6} \cdot 8}{q^{6} (- q^{3})}$

Cancel the common factor.

$\frac{q^{6} \cdot 8}{q^{6} (- q^{3})}$

Rewrite the expression.

$\frac{8}{- q^{3}}$

Step 4

Move the negative in front of the fraction.

$- \frac{8}{q^{3}}$