Simplify ((3r^6n^3)/(2r^5n))^4

${(\frac{3 r^{6} n^{3}}{2 r^{5} n})}^{4}$

Cancel the common factor of $r^{6}$ and $r^{5}$ .

Factor $r^{5}$ out of $3 r^{6} n^{3}$ .

${(\frac{r^{5} (3 r n^{3})}{2 r^{5} n})}^{4}$

Cancel the common factors.

Factor $r^{5}$ out of $2 r^{5} n$ .

${(\frac{r^{5} (3 r n^{3})}{r^{5} (2 n)})}^{4}$

Cancel the common factor.

${(\frac{r^{5} (3 r n^{3})}{r^{5} (2 n)})}^{4}$

Rewrite the expression.

${(\frac{3 r n^{3}}{2 n})}^{4}$

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

Factor $n$ out of $3 r n^{3}$ .

${(\frac{n (3 r n^{2})}{2 n})}^{4}$

Cancel the common factors.

Factor $n$ out of $2 n$ .

${(\frac{n (3 r n^{2})}{n \cdot 2})}^{4}$

Cancel the common factor.

${(\frac{n (3 r n^{2})}{n \cdot 2})}^{4}$

Rewrite the expression.

${(\frac{3 r n^{2}}{2})}^{4}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{3 r n^{2}}{2}$ .

$\frac{{(3 r n^{2})}^{4}}{2^{4}}$

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

$\frac{{(3 r)}^{4} {(n^{2})}^{4}}{2^{4}}$

Apply the product rule to $3 r$ .

$\frac{3^{4} r^{4} {(n^{2})}^{4}}{2^{4}}$

Simplify the numerator.

Raise $3$ to the power of $4$ .

$\frac{81 r^{4} {(n^{2})}^{4}}{2^{4}}$

Multiply the exponents in ${(n^{2})}^{4}$ .

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

$\frac{81 r^{4} n^{2 \cdot 4}}{2^{4}}$

Multiply $2$ by $4$ .

$\frac{81 r^{4} n^{8}}{2^{4}}$

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

$\frac{81 r^{4} n^{8}}{16}$