Algebra Examples

$(5 x^{6} y) (2 y^{3}) (3 x^{- 2} y^{- 9})$

Step 1

Multiply $x^{6}$ by $x^{- 2}$ by adding the exponents.

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Step 1.1

Move $x^{- 2}$ .

$5 (x^{- 2} x^{6}) y (2 y^{3}) (3 y^{- 9})$

Step 1.2

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

$5 x^{- 2 + 6} y (2 y^{3}) (3 y^{- 9})$

Step 1.3

Add $- 2$ and $6$ .

$5 x^{4} y (2 y^{3}) (3 y^{- 9})$

Step 2

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

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Step 2.1

Move $y^{3}$ .

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

Step 2.2

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

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Step 2.2.1

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

$5 x^{4} (y^{3} y^{1}) \cdot 2 (3 y^{- 9})$

Step 2.2.2

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

$5 x^{4} y^{3 + 1} \cdot 2 (3 y^{- 9})$

Step 2.3

Add $3$ and $1$ .

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

Step 3

Multiply $y^{4}$ by $y^{- 9}$ by adding the exponents.

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Step 3.1

Move $y^{- 9}$ .

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

Step 3.2

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

$5 x^{4} y^{- 9 + 4} \cdot 2 \cdot 3$

Step 3.3

Add $- 9$ and $4$ .

$5 x^{4} y^{- 5} \cdot 2 \cdot 3$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$5 x^{4} \frac{1}{y^{5}} \cdot 2 \cdot 3$

Step 5

Multiply $5 x^{4} \frac{1}{y^{5}}$ .

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Step 5.1

Combine $5$ and $\frac{1}{y^{5}}$ .

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

Step 5.2

Combine $x^{4}$ and $\frac{5}{y^{5}}$ .

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

Step 6

Move $5$ to the left of $x^{4}$ .

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

Step 7

Multiply $\frac{5 x^{4}}{y^{5}} \cdot 2$ .

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Step 7.1

Combine $\frac{5 x^{4}}{y^{5}}$ and $2$ .

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

Step 7.2

Multiply $2$ by $5$ .

$\frac{10 x^{4}}{y^{5}} \cdot 3$

Step 8

Multiply $\frac{10 x^{4}}{y^{5}} \cdot 3$ .

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Step 8.1

Combine $\frac{10 x^{4}}{y^{5}}$ and $3$ .

$\frac{10 x^{4} \cdot 3}{y^{5}}$

Step 8.2

Multiply $3$ by $10$ .

$\frac{30 x^{4}}{y^{5}}$