Simplify ((g^2)/(5f^2))/(g/(f^3))

$\frac{\frac{g^{2}}{5 f^{2}}}{\frac{g}{f^{3}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{g^{2}}{5 f^{2}} \cdot \frac{f^{3}}{g}$

Step 2

Combine.

$\frac{g^{2} f^{3}}{5 f^{2} g}$

Step 3

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

Factor $g$ out of $g^{2} f^{3}$ .

$\frac{g (g f^{3})}{5 f^{2} g}$

Cancel the common factors.

Factor $g$ out of $5 f^{2} g$ .

$\frac{g (g f^{3})}{g (5 f^{2})}$

Cancel the common factor.

$\frac{g (g f^{3})}{g (5 f^{2})}$

Rewrite the expression.

$\frac{g f^{3}}{5 f^{2}}$

Step 4

Cancel the common factor of $f^{3}$ and $f^{2}$ .

Factor $f^{2}$ out of $g f^{3}$ .

$\frac{f^{2} (g f)}{5 f^{2}}$

Cancel the common factors.

Factor $f^{2}$ out of $5 f^{2}$ .

$\frac{f^{2} (g f)}{f^{2} \cdot 5}$

Cancel the common factor.

$\frac{f^{2} (g f)}{f^{2} \cdot 5}$

Rewrite the expression.

$\frac{g f}{5}$