Simplify (8/(2n^3))÷4n^2

$\frac{8}{2 n^{3}} \div 4 n^{2}$

Rewrite the division as a fraction.

$\frac{\frac{8}{2 n^{3}}}{4 n^{2}}$

Cancel the common factor of $8$ and $2$ .

Factor $2$ out of $8$ .

$\frac{\frac{2 \cdot 4}{2 n^{3}}}{4 n^{2}}$

Cancel the common factors.

Factor $2$ out of $2 n^{3}$ .

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

Cancel the common factor.

$\frac{\frac{2 \cdot 4}{2 n^{3}}}{4 n^{2}}$

Rewrite the expression.

$\frac{\frac{4}{n^{3}}}{4 n^{2}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{4}{n^{3}} \cdot \frac{1}{4 n^{2}}$

Combine.

$\frac{4 \cdot 1}{n^{3} (4 n^{2})}$

Multiply $n^{3}$ by $n^{2}$ by adding the exponents.

Move $n^{2}$ .

$\frac{4 \cdot 1}{n^{2} n^{3} \cdot 4}$

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

$\frac{4 \cdot 1}{n^{2 + 3} \cdot 4}$

Add $2$ and $3$ .

$\frac{4 \cdot 1}{n^{5} \cdot 4}$

Multiply $4$ by $1$ .

$\frac{4}{n^{5} \cdot 4}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{n^{5} \cdot 4}$

Rewrite the expression.

$\frac{1}{n^{5}}$