Algebra Examples

$\frac{10 x^{3}}{8 y^{3}} \cdot \frac{16 x}{15 y^{2}} \cdot \frac{9 y^{4}}{x^{3}}$

Step 1

Combine.

$\frac{10 x^{3} (16 x)}{8 y^{3} (15 y^{2})} \cdot \frac{9 y^{4}}{x^{3}}$

Step 2

Combine.

$\frac{10 x^{3} (16 x) (9 y^{4})}{8 y^{3} (15 y^{2}) x^{3}}$

Step 3

Multiply $x^{3}$ by $x$ by adding the exponents.

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Step 3.1

Move $x$ .

$\frac{10 (x \cdot x^{3}) \cdot 16 (9 y^{4})}{8 y^{3} (15 y^{2}) x^{3}}$

Step 3.2

Multiply $x$ by $x^{3}$ .

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Step 3.2.1

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

$\frac{10 (x^{1} x^{3}) \cdot 16 (9 y^{4})}{8 y^{3} (15 y^{2}) x^{3}}$

Step 3.2.2

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

$\frac{10 x^{1 + 3} \cdot 16 (9 y^{4})}{8 y^{3} (15 y^{2}) x^{3}}$

Step 3.3

Add $1$ and $3$ .

$\frac{10 x^{4} \cdot 16 (9 y^{4})}{8 y^{3} (15 y^{2}) x^{3}}$

Step 4

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

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Step 4.1

Move $y^{2}$ .

$\frac{10 x^{4} \cdot 16 (9 y^{4})}{8 (y^{2} y^{3}) \cdot 15 x^{3}}$

Step 4.2

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

$\frac{10 x^{4} \cdot 16 (9 y^{4})}{8 y^{2 + 3} \cdot 15 x^{3}}$

Step 4.3

Add $2$ and $3$ .

$\frac{10 x^{4} \cdot 16 (9 y^{4})}{8 y^{5} \cdot 15 x^{3}}$

Step 5

Cancel the common factor of $10$ and $8$ .

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Step 5.1

Factor $2$ out of $10 x^{4} \cdot 16 (9 y^{4})$ .

$\frac{2 (5 x^{4} \cdot 16 (9 y^{4}))}{8 y^{5} \cdot 15 x^{3}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $8 y^{5} \cdot 15 x^{3}$ .

$\frac{2 (5 x^{4} \cdot 16 (9 y^{4}))}{2 (4 y^{5} \cdot 15 x^{3})}$

Step 5.2.2

Cancel the common factor.

$\frac{2 (5 x^{4} \cdot 16 (9 y^{4}))}{2 (4 y^{5} \cdot 15 x^{3})}$

Step 5.2.3

Rewrite the expression.

$\frac{5 x^{4} \cdot 16 (9 y^{4})}{4 y^{5} \cdot 15 x^{3}}$

Step 6

Cancel the common factor of $5$ and $15$ .

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Step 6.1

Factor $5$ out of $5 x^{4} \cdot 16 (9 y^{4})$ .

$\frac{5 (x^{4} \cdot 16 (9 y^{4}))}{4 y^{5} \cdot 15 x^{3}}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $5$ out of $4 y^{5} \cdot 15 x^{3}$ .

$\frac{5 (x^{4} \cdot 16 (9 y^{4}))}{5 (4 y^{5} \cdot 3 x^{3})}$

Step 6.2.2

Cancel the common factor.

$\frac{5 (x^{4} \cdot 16 (9 y^{4}))}{5 (4 y^{5} \cdot 3 x^{3})}$

Step 6.2.3

Rewrite the expression.

$\frac{x^{4} \cdot 16 (9 y^{4})}{4 y^{5} \cdot 3 x^{3}}$

Step 7

Cancel the common factor of $x^{4}$ and $x^{3}$ .

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Step 7.1

Factor $x^{3}$ out of $x^{4} \cdot 16 (9 y^{4})$ .

$\frac{x^{3} (x \cdot 16 (9 y^{4}))}{4 y^{5} \cdot 3 x^{3}}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $x^{3}$ out of $4 y^{5} \cdot 3 x^{3}$ .

$\frac{x^{3} (x \cdot 16 (9 y^{4}))}{x^{3} (4 y^{5} \cdot 3)}$

Step 7.2.2

Cancel the common factor.

$\frac{x^{3} (x \cdot 16 (9 y^{4}))}{x^{3} (4 y^{5} \cdot 3)}$

Step 7.2.3

Rewrite the expression.

$\frac{x \cdot 16 (9 y^{4})}{4 y^{5} \cdot 3}$

Step 8

Cancel the common factor of $16$ and $4$ .

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Step 8.1

Factor $4$ out of $x \cdot 16 (9 y^{4})$ .

$\frac{4 (x \cdot 4 (9 y^{4}))}{4 y^{5} \cdot 3}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $4$ out of $4 y^{5} \cdot 3$ .

$\frac{4 (x \cdot 4 (9 y^{4}))}{4 (y^{5} \cdot 3)}$

Step 8.2.2

Cancel the common factor.

$\frac{4 (x \cdot 4 (9 y^{4}))}{4 (y^{5} \cdot 3)}$

Step 8.2.3

Rewrite the expression.

$\frac{x \cdot 4 (9 y^{4})}{y^{5} \cdot 3}$

Step 9

Cancel the common factor of $9$ and $3$ .

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Step 9.1

Factor $3$ out of $x \cdot 4 (9 y^{4})$ .

$\frac{3 (x \cdot 4 (3 y^{4}))}{y^{5} \cdot 3}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $3$ out of $y^{5} \cdot 3$ .

$\frac{3 (x \cdot 4 (3 y^{4}))}{3 \cdot y^{5}}$

Step 9.2.2

Cancel the common factor.

$\frac{3 (x \cdot 4 (3 y^{4}))}{3 \cdot y^{5}}$

Step 9.2.3

Rewrite the expression.

$\frac{x \cdot 4 (3 y^{4})}{y^{5}}$

Step 10

Cancel the common factor of $y^{4}$ and $y^{5}$ .

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Step 10.1

Factor $y^{4}$ out of $x \cdot 4 (3 y^{4})$ .

$\frac{y^{4} (x \cdot 4 \cdot (3))}{y^{5}}$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $y^{4}$ out of $y^{5}$ .

$\frac{y^{4} (x \cdot 4 \cdot (3))}{y^{4} y}$

Step 10.2.2

Cancel the common factor.

$\frac{y^{4} (x \cdot 4 \cdot (3))}{y^{4} y}$

Step 10.2.3

Rewrite the expression.

$\frac{x \cdot 4 \cdot (3)}{y}$

Step 11

Simplify the expression.

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Step 11.1

Multiply $3$ by $4$ .

$\frac{x \cdot 12}{y}$

Step 11.2

Move $12$ to the left of $x$ .

$\frac{12 x}{y}$