Write the Fraction in Simplest Form (15q)/((3q^3)^2)

$\frac{15 q}{{(3 q^{3})}^{2}}$

Step 1

Simplify the denominator.

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

$\frac{15 q}{3^{2} {(q^{3})}^{2}}$

Raise $3$ to the power of $2$ .

$\frac{15 q}{9 {(q^{3})}^{2}}$

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

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

$\frac{15 q}{9 q^{3 \cdot 2}}$

Multiply $3$ by $2$ .

$\frac{15 q}{9 q^{6}}$

Step 2

Cancel the common factor of $15$ and $9$ .

Factor $3$ out of $15 q$ .

$\frac{3 (5 q)}{9 q^{6}}$

Cancel the common factors.

Factor $3$ out of $9 q^{6}$ .

$\frac{3 (5 q)}{3 (3 q^{6})}$

Cancel the common factor.

$\frac{3 (5 q)}{3 (3 q^{6})}$

Rewrite the expression.

$\frac{5 q}{3 q^{6}}$

Step 3

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

Factor $q$ out of $5 q$ .

$\frac{q \cdot 5}{3 q^{6}}$

Cancel the common factors.

Factor $q$ out of $3 q^{6}$ .

$\frac{q \cdot 5}{q (3 q^{5})}$

Cancel the common factor.

$\frac{q \cdot 5}{q (3 q^{5})}$

Rewrite the expression.

$\frac{5}{3 q^{5}}$