Algebra Examples

$\frac{- 3 x^{5}}{x^{13}} \cdot \frac{2 x^{- 10} y}{15 y^{- 2}}$

Step 1

Combine.

$\frac{- 3 x^{5} (2 x^{- 10} y)}{x^{13} (15 y^{- 2})}$

Step 2

Multiply $x^{5}$ by $x^{- 10}$ by adding the exponents.

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Step 2.1

Move $x^{- 10}$ .

$\frac{- 3 (x^{- 10} x^{5}) (2 y)}{x^{13} (15 y^{- 2})}$

Step 2.2

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

$\frac{- 3 x^{- 10 + 5} (2 y)}{x^{13} (15 y^{- 2})}$

Step 2.3

Add $- 10$ and $5$ .

$\frac{- 3 x^{- 5} (2 y)}{x^{13} (15 y^{- 2})}$

Step 3

Move $x^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 3 (2 y)}{x^{13} (15 y^{- 2}) x^{5}}$

Step 4

Multiply $x^{13}$ by $x^{5}$ by adding the exponents.

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Step 4.1

Move $x^{5}$ .

$\frac{- 3 (2 y)}{x^{5} x^{13} (15 y^{- 2})}$

Step 4.2

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

$\frac{- 3 (2 y)}{x^{5 + 13} (15 y^{- 2})}$

Step 4.3

Add $5$ and $13$ .

$\frac{- 3 (2 y)}{x^{18} (15 y^{- 2})}$

Step 5

Move $y^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{- 3 (2 y) y^{2}}{x^{18} \cdot 15}$

Step 6

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

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Step 6.1

Move $y^{2}$ .

$\frac{- 3 (2 (y^{2} y))}{x^{18} \cdot 15}$

Step 6.2

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

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Step 6.2.1

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

$\frac{- 3 (2 (y^{2} y^{1}))}{x^{18} \cdot 15}$

Step 6.2.2

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

$\frac{- 3 (2 y^{2 + 1})}{x^{18} \cdot 15}$

Step 6.3

Add $2$ and $1$ .

$\frac{- 3 (2 y^{3})}{x^{18} \cdot 15}$

Step 7

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

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Step 7.1

Factor $3$ out of $- 3 (2 y^{3})$ .

$\frac{3 (- (2 y^{3}))}{x^{18} \cdot 15}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $3$ out of $x^{18} \cdot 15$ .

$\frac{3 (- (2 y^{3}))}{3 (x^{18} \cdot 5)}$

Step 7.2.2

Cancel the common factor.

$\frac{3 (- (2 y^{3}))}{3 (x^{18} \cdot 5)}$

Step 7.2.3

Rewrite the expression.

$\frac{- (2 y^{3})}{x^{18} \cdot 5}$

Step 8

Simplify the expression.

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Step 8.1

Multiply $- 1$ by $2$ .

$\frac{- 2 y^{3}}{x^{18} \cdot 5}$

Step 8.2

Move $5$ to the left of $x^{18}$ .

$\frac{- 2 y^{3}}{5 \cdot x^{18}}$

Step 8.3

Move the negative in front of the fraction.

$- \frac{2 y^{3}}{5 x^{18}}$