Algebra Examples

$\frac{72 x^{2}}{25 y^{5}} \cdot (- \frac{2.5 y^{4}}{27 x^{5}})$

Step 1

Rewrite using the commutative property of multiplication.

$- \frac{72 x^{2}}{25 y^{5}} \cdot \frac{2.5 y^{4}}{27 x^{5}}$

Step 2

Cancel the common factor of $9 x^{2}$ .

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Step 2.1

Move the leading negative in $- \frac{72 x^{2}}{25 y^{5}}$ into the numerator.

$\frac{- 72 x^{2}}{25 y^{5}} \cdot \frac{2.5 y^{4}}{27 x^{5}}$

Step 2.2

Factor $9 x^{2}$ out of $- 72 x^{2}$ .

$\frac{9 x^{2} (- 8)}{25 y^{5}} \cdot \frac{2.5 y^{4}}{27 x^{5}}$

Step 2.3

Factor $9 x^{2}$ out of $27 x^{5}$ .

$\frac{9 x^{2} (- 8)}{25 y^{5}} \cdot \frac{2.5 y^{4}}{9 x^{2} (3 x^{3})}$

Step 2.4

Cancel the common factor.

$\frac{9 x^{2} \cdot - 8}{25 y^{5}} \cdot \frac{2.5 y^{4}}{9 x^{2} (3 x^{3})}$

Step 2.5

Rewrite the expression.

$\frac{- 8}{25 y^{5}} \cdot \frac{2.5 y^{4}}{3 x^{3}}$

Step 3

Cancel the common factor of $2.5 y^{4}$ .

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Step 3.1

Factor $2.5 y^{4}$ out of $25 y^{5}$ .

$\frac{- 8}{2.5 y^{4} (10 y)} \cdot \frac{2.5 y^{4}}{3 x^{3}}$

Step 3.2

Cancel the common factor.

$\frac{- 8}{2.5 y^{4} (10 y)} \cdot \frac{2.5 y^{4}}{3 x^{3}}$

Step 3.3

Rewrite the expression.

$\frac{- 8}{10 y} \cdot \frac{1}{3 x^{3}}$

Step 4

Multiply $\frac{- 8}{10 y}$ by $\frac{1}{3 x^{3}}$ .

$\frac{- 8}{10 y (3 x^{3})}$

Step 5

Multiply $3$ by $10$ .

$\frac{- 8}{30 y x^{3}}$

Step 6

Cancel the common factor of $- 8$ and $30$ .

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Step 6.1

Factor $2$ out of $- 8$ .

$\frac{2 (- 4)}{30 y x^{3}}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $30 y x^{3}$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

$\frac{- 4}{15 y x^{3}}$

Step 7

Move the negative in front of the fraction.

$- \frac{4}{15 y x^{3}}$