Simplify (8/(r^3s^2))÷(6/(rs^4))

$\frac{8}{r^{3} s^{2}} \div \frac{6}{r s^{4}}$

To divide by a fraction, multiply by its reciprocal.

$\frac{8}{r^{3} s^{2}} \cdot \frac{r s^{4}}{6}$

Combine.

$\frac{8 (r s^{4})}{r^{3} s^{2} \cdot 6}$

Cancel the common factor of $8$ and $6$ .

Factor $2$ out of $8 (r s^{4})$ .

$\frac{2 (4 (r s^{4}))}{r^{3} s^{2} \cdot 6}$

Cancel the common factors.

Factor $2$ out of $r^{3} s^{2} \cdot 6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Factor $r$ out of $4 (r s^{4})$ .

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

Cancel the common factors.

Factor $r$ out of $r^{3} s^{2} \cdot 3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Cancel the common factor of $s^{4}$ and $s^{2}$ .

Factor $s^{2}$ out of $4 (s^{4})$ .

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

Cancel the common factors.

Factor $s^{2}$ out of $r^{2} s^{2} \cdot 3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Move $3$ to the left of $r^{2}$ .

$\frac{4 s^{2}}{3 r^{2}}$

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