Algebra Examples

$\frac{10 x^{3}}{7 y^{3}} \cdot \frac{14 x}{15 y^{2}} \cdot \frac{15 y^{4}}{x^{3}}$

Step 1

Combine.

$\frac{10 x^{3} (14 x)}{7 y^{3} (15 y^{2})} \cdot \frac{15 y^{4}}{x^{3}}$

Step 2

Combine.

$\frac{10 x^{3} (14 x) (15 y^{4})}{7 y^{3} (15 y^{2}) x^{3}}$

Step 3

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

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Step 3.1

Move $x$ .

$\frac{10 (x \cdot x^{3}) \cdot 14 (15 y^{4})}{7 y^{3} (15 y^{2}) x^{3}}$

Step 3.2

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

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Step 3.2.1

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

$\frac{10 (x^{1} x^{3}) \cdot 14 (15 y^{4})}{7 y^{3} (15 y^{2}) x^{3}}$

Step 3.2.2

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

$\frac{10 x^{1 + 3} \cdot 14 (15 y^{4})}{7 y^{3} (15 y^{2}) x^{3}}$

Step 3.3

Add $1$ and $3$ .

$\frac{10 x^{4} \cdot 14 (15 y^{4})}{7 y^{3} (15 y^{2}) x^{3}}$

Step 4

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

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Step 4.1

Move $y^{2}$ .

$\frac{10 x^{4} \cdot 14 (15 y^{4})}{7 (y^{2} y^{3}) \cdot 15 x^{3}}$

Step 4.2

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

$\frac{10 x^{4} \cdot 14 (15 y^{4})}{7 y^{2 + 3} \cdot 15 x^{3}}$

Step 4.3

Add $2$ and $3$ .

$\frac{10 x^{4} \cdot 14 (15 y^{4})}{7 y^{5} \cdot 15 x^{3}}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Cancel the common factor of $10$ and $15$ .

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Step 5.1.1

Factor $5$ out of $10 x^{4} \cdot 14 (15 y^{4})$ .

$\frac{5 (2 x^{4} \cdot 14 (15 y^{4}))}{7 y^{5} \cdot 15 x^{3}}$

Step 5.1.2

Cancel the common factors.

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Step 5.1.2.1

Factor $5$ out of $7 y^{5} \cdot 15 x^{3}$ .

$\frac{5 (2 x^{4} \cdot 14 (15 y^{4}))}{5 (7 y^{5} \cdot 3 x^{3})}$

Step 5.1.2.2

Cancel the common factor.

$\frac{5 (2 x^{4} \cdot 14 (15 y^{4}))}{5 (7 y^{5} \cdot 3 x^{3})}$

Step 5.1.2.3

Rewrite the expression.

$\frac{2 x^{4} \cdot 14 (15 y^{4})}{7 y^{5} \cdot 3 x^{3}}$

Step 5.2

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

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Step 5.2.1

Factor $x^{3}$ out of $2 x^{4} \cdot 14 (15 y^{4})$ .

$\frac{x^{3} (2 x \cdot 14 (15 y^{4}))}{7 y^{5} \cdot 3 x^{3}}$

Step 5.2.2

Cancel the common factors.

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Step 5.2.2.1

Factor $x^{3}$ out of $7 y^{5} \cdot 3 x^{3}$ .

$\frac{x^{3} (2 x \cdot 14 (15 y^{4}))}{x^{3} (7 y^{5} \cdot 3)}$

Step 5.2.2.2

Cancel the common factor.

$\frac{x^{3} (2 x \cdot 14 (15 y^{4}))}{x^{3} (7 y^{5} \cdot 3)}$

Step 5.2.2.3

Rewrite the expression.

$\frac{2 x \cdot 14 (15 y^{4})}{7 y^{5} \cdot 3}$

Step 5.3

Cancel the common factor of $14$ and $7$ .

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Step 5.3.1

Factor $7$ out of $2 x \cdot 14 (15 y^{4})$ .

$\frac{7 (2 x \cdot 2 (15 y^{4}))}{7 y^{5} \cdot 3}$

Step 5.3.2

Cancel the common factors.

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Step 5.3.2.1

Factor $7$ out of $7 y^{5} \cdot 3$ .

$\frac{7 (2 x \cdot 2 (15 y^{4}))}{7 (y^{5} \cdot 3)}$

Step 5.3.2.2

Cancel the common factor.

$\frac{7 (2 x \cdot 2 (15 y^{4}))}{7 (y^{5} \cdot 3)}$

Step 5.3.2.3

Rewrite the expression.

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

Step 5.4

Cancel the common factor of $15$ and $3$ .

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Step 5.4.1

Factor $3$ out of $2 x \cdot 2 (15 y^{4})$ .

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

Step 5.4.2

Cancel the common factors.

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Step 5.4.2.1

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

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

Step 5.4.2.2

Cancel the common factor.

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

Step 5.4.2.3

Rewrite the expression.

$\frac{2 x \cdot 2 (5 y^{4})}{y^{5}}$

Step 5.5

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

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Step 5.5.1

Factor $y^{4}$ out of $2 x \cdot 2 (5 y^{4})$ .

$\frac{y^{4} (2 x \cdot 2 \cdot (5))}{y^{5}}$

Step 5.5.2

Cancel the common factors.

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Step 5.5.2.1

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

$\frac{y^{4} (2 x \cdot 2 \cdot (5))}{y^{4} y}$

Step 5.5.2.2

Cancel the common factor.

$\frac{y^{4} (2 x \cdot 2 \cdot (5))}{y^{4} y}$

Step 5.5.2.3

Rewrite the expression.

$\frac{2 x \cdot 2 \cdot (5)}{y}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $2$ by $2$ .

$\frac{4 x \cdot 5}{y}$

Step 6.2

Multiply $5$ by $4$ .

$\frac{20 x}{y}$