Write the Fraction in Simplest Form (12q^3)/((3q^2)^5)

$\frac{12 q^{3}}{{(3 q^{2})}^{5}}$

Step 1

Simplify the denominator.

Apply the product rule to $3 q^{2}$ .

$\frac{12 q^{3}}{3^{5} {(q^{2})}^{5}}$

Raise $3$ to the power of $5$ .

$\frac{12 q^{3}}{243 {(q^{2})}^{5}}$

Multiply the exponents in ${(q^{2})}^{5}$ .

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

$\frac{12 q^{3}}{243 q^{2 \cdot 5}}$

Multiply $2$ by $5$ .

$\frac{12 q^{3}}{243 q^{10}}$

Step 2

Cancel the common factor of $12$ and $243$ .

Factor $3$ out of $12 q^{3}$ .

$\frac{3 (4 q^{3})}{243 q^{10}}$

Cancel the common factors.

Factor $3$ out of $243 q^{10}$ .

$\frac{3 (4 q^{3})}{3 (81 q^{10})}$

Cancel the common factor.

$\frac{3 (4 q^{3})}{3 (81 q^{10})}$

Rewrite the expression.

$\frac{4 q^{3}}{81 q^{10}}$

Step 3

Cancel the common factor of $q^{3}$ and $q^{10}$ .

Factor $q^{3}$ out of $4 q^{3}$ .

$\frac{q^{3} \cdot 4}{81 q^{10}}$

Cancel the common factors.

Factor $q^{3}$ out of $81 q^{10}$ .

$\frac{q^{3} \cdot 4}{q^{3} (81 q^{7})}$

Cancel the common factor.

$\frac{q^{3} \cdot 4}{q^{3} (81 q^{7})}$

Rewrite the expression.

$\frac{4}{81 q^{7}}$