Algebra Examples

$\frac{x y^{9}}{3 y^{- 2}} \cdot \frac{- 7 y}{21 x^{5}}$

Step 1

Combine.

$\frac{x y^{9} (- 7 y)}{3 y^{- 2} (21 x^{5})}$

Step 2

Multiply $y^{9}$ by $y$ by adding the exponents.

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Step 2.1

Move $y$ .

$\frac{x (y \cdot y^{9}) \cdot - 7}{3 y^{- 2} (21 x^{5})}$

Step 2.2

Multiply $y$ by $y^{9}$ .

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Step 2.2.1

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

$\frac{x (y^{1} y^{9}) \cdot - 7}{3 y^{- 2} (21 x^{5})}$

Step 2.2.2

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

$\frac{x y^{1 + 9} \cdot - 7}{3 y^{- 2} (21 x^{5})}$

Step 2.3

Add $1$ and $9$ .

$\frac{x y^{10} \cdot - 7}{3 y^{- 2} (21 x^{5})}$

Step 3

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

$\frac{x y^{10} \cdot - 7 y^{2}}{3 (21 x^{5})}$

Step 4

Multiply $y^{10}$ by $y^{2}$ by adding the exponents.

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Step 4.1

Move $y^{2}$ .

$\frac{x (y^{2} y^{10}) \cdot - 7}{3 (21 x^{5})}$

Step 4.2

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

$\frac{x y^{2 + 10} \cdot - 7}{3 (21 x^{5})}$

Step 4.3

Add $2$ and $10$ .

$\frac{x y^{12} \cdot - 7}{3 (21 x^{5})}$

Step 5

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

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Step 5.1

Factor $x$ out of $x y^{12} \cdot - 7$ .

$\frac{x (y^{12} \cdot - 7)}{3 (21 x^{5})}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $x$ out of $3 (21 x^{5})$ .

$\frac{x (y^{12} \cdot - 7)}{x (3 (21 x^{4}))}$

Step 5.2.2

Cancel the common factor.

$\frac{x (y^{12} \cdot - 7)}{x (3 (21 x^{4}))}$

Step 5.2.3

Rewrite the expression.

$\frac{y^{12} \cdot - 7}{3 (21 x^{4})}$

Step 6

Cancel the common factor of $- 7$ and $21$ .

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Step 6.1

Factor $7$ out of $y^{12} \cdot - 7$ .

$\frac{7 (y^{12} \cdot - 1)}{3 (21 x^{4})}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $7$ out of $3 (21 x^{4})$ .

$\frac{7 (y^{12} \cdot - 1)}{7 (3 (3 x^{4}))}$

Step 6.2.2

Cancel the common factor.

$\frac{7 (y^{12} \cdot - 1)}{7 (3 (3 x^{4}))}$

Step 6.2.3

Rewrite the expression.

$\frac{y^{12} \cdot - 1}{3 (3 x^{4})}$

Step 7

Simplify the expression.

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Step 7.1

Multiply $3$ by $3$ .

$\frac{y^{12} \cdot - 1}{3^{2} x^{4}}$

Step 7.2

Raise $3$ to the power of $2$ .

$\frac{y^{12} \cdot - 1}{9 x^{4}}$

Step 7.3

Move $- 1$ to the left of $y^{12}$ .

$\frac{- 1 \cdot y^{12}}{9 x^{4}}$

Step 7.4

Move the negative in front of the fraction.

$- \frac{y^{12}}{9 x^{4}}$