Simplify (24g^3)/(5f^2)*(10(gf)^3)/(8g^5f)

$\frac{24 g^{3}}{5 f^{2}} \cdot \frac{10 {(g f)}^{3}}{8 g^{5} f}$

Combine.

$\frac{24 g^{3} (10 {(g f)}^{3})}{5 f^{2} (8 g^{5} f)}$

Multiply $f^{2}$ by $f$ by adding the exponents.

Move $f$ .

$\frac{24 g^{3} (10 {(g f)}^{3})}{5 (f \cdot f^{2}) (8 g^{5})}$

Multiply $f$ by $f^{2}$ .

Raise $f$ to the power of $1$ .

$\frac{24 g^{3} (10 {(g f)}^{3})}{5 (f^{1} f^{2}) (8 g^{5})}$

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

$\frac{24 g^{3} (10 {(g f)}^{3})}{5 f^{1 + 2} (8 g^{5})}$

Add $1$ and $2$ .

$\frac{24 g^{3} (10 {(g f)}^{3})}{5 f^{3} (8 g^{5})}$

Cancel the common factor of $24$ and $8$ .

Factor $8$ out of $24 g^{3} (10 {(g f)}^{3})$ .

$\frac{8 (3 g^{3} (10 {(g f)}^{3}))}{5 f^{3} (8 g^{5})}$

Cancel the common factors.

Factor $8$ out of $5 f^{3} (8 g^{5})$ .

$\frac{8 (3 g^{3} (10 {(g f)}^{3}))}{8 (5 f^{3} (g^{5}))}$

Cancel the common factor.

$\frac{8 (3 g^{3} (10 {(g f)}^{3}))}{8 (5 f^{3} (g^{5}))}$

Rewrite the expression.

$\frac{3 g^{3} (10 {(g f)}^{3})}{5 f^{3} (g^{5})}$

Cancel the common factor of $g^{3}$ and $g^{5}$ .

Factor $g^{3}$ out of $3 g^{3} (10 {(g f)}^{3})$ .

$\frac{g^{3} (3 (10 {(g f)}^{3}))}{5 f^{3} (g^{5})}$

Cancel the common factors.

Factor $g^{3}$ out of $5 f^{3} (g^{5})$ .

$\frac{g^{3} (3 (10 {(g f)}^{3}))}{g^{3} (5 f^{3} (g^{2}))}$

Cancel the common factor.

$\frac{g^{3} (3 (10 {(g f)}^{3}))}{g^{3} (5 f^{3} (g^{2}))}$

Rewrite the expression.

$\frac{3 (10 {(g f)}^{3})}{5 f^{3} (g^{2})}$

Cancel the common factor of $10$ and $5$ .

Factor $5$ out of $3 (10 {(g f)}^{3})$ .

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

Cancel the common factors.

Factor $5$ out of $5 f^{3} (g^{2})$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $3$ by $2$ .

$\frac{6 {(g f)}^{3}}{f^{3} g^{2}}$

Apply the product rule to $g f$ .

$\frac{6 g^{3} f^{3}}{f^{3} g^{2}}$

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

Factor $g^{2}$ out of $6 g^{3} f^{3}$ .

$\frac{g^{2} (6 g f^{3})}{f^{3} g^{2}}$

Cancel the common factors.

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

$\frac{g^{2} (6 g f^{3})}{g^{2} f^{3}}$

Cancel the common factor.

$\frac{g^{2} (6 g f^{3})}{g^{2} f^{3}}$

Rewrite the expression.

$\frac{6 g f^{3}}{f^{3}}$

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

Cancel the common factor.

$\frac{6 g f^{3}}{f^{3}}$

Divide $6 g$ by $1$ .

$6 g$

Simplify (24g^3)/(5f^2)*(10(gf)^3)/(8g^5f)

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