Algebra Examples

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

Step 1

Combine.

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

Step 2

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

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Step 2.1

Move $f$ .

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.3

Add $1$ and $2$ .

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

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

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Step 5.1

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

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

Step 6

Multiply $3$ by $2$ .

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

Step 7

Apply the product rule to $g f$ .

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

Step 8

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

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Step 8.1

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

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

Step 8.2

Cancel the common factors.

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Step 8.2.1

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

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

Step 8.2.2

Cancel the common factor.

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

Step 8.2.3

Rewrite the expression.

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

Step 9

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

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Step 9.1

Cancel the common factor.

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

Step 9.2

Divide $6 g$ by $1$ .

$6 g$