Algebra Examples

$(2 x^{2} y^{- 5}) (6 x^{- 3} y) (\frac{1}{3} x^{- 1} y^{3})$

Step 1

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

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Step 1.1

Move $x^{- 3}$ .

$2 (x^{- 3} x^{2}) y^{- 5} (6 y) (\frac{1}{3} \cdot (x^{- 1} y^{3}))$

Step 1.2

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

$2 x^{- 3 + 2} y^{- 5} (6 y) (\frac{1}{3} \cdot (x^{- 1} y^{3}))$

Step 1.3

Add $- 3$ and $2$ .

$2 x^{- 1} y^{- 5} (6 y) (\frac{1}{3} \cdot (x^{- 1} y^{3}))$

Step 2

Multiply $x^{- 1}$ by $x^{- 1}$ by adding the exponents.

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Step 2.1

Move $x^{- 1}$ .

$2 (x^{- 1} x^{- 1}) y^{- 5} (6 y) (\frac{1}{3} \cdot (y^{3}))$

Step 2.2

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

$2 x^{- 1 - 1} y^{- 5} (6 y) (\frac{1}{3} \cdot (y^{3}))$

Step 2.3

Subtract $1$ from $- 1$ .

$2 x^{- 2} y^{- 5} (6 y) (\frac{1}{3} \cdot (y^{3}))$

Step 3

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

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Step 3.1

Move $y$ .

$2 x^{- 2} (y \cdot y^{- 5}) \cdot 6 (\frac{1}{3} \cdot (y^{3}))$

Step 3.2

Multiply $y$ by $y^{- 5}$ .

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Step 3.2.1

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

$2 x^{- 2} (y^{1} y^{- 5}) \cdot 6 (\frac{1}{3} \cdot (y^{3}))$

Step 3.2.2

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

$2 x^{- 2} y^{1 - 5} \cdot 6 (\frac{1}{3} \cdot (y^{3}))$

Step 3.3

Subtract $5$ from $1$ .

$2 x^{- 2} y^{- 4} \cdot 6 (\frac{1}{3} \cdot (y^{3}))$

Step 4

Multiply $y^{- 4}$ by $y^{3}$ by adding the exponents.

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Step 4.1

Move $y^{3}$ .

$2 x^{- 2} (y^{3} y^{- 4}) \cdot 6 \frac{1}{3}$

Step 4.2

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

$2 x^{- 2} y^{3 - 4} \cdot 6 \frac{1}{3}$

Step 4.3

Subtract $4$ from $3$ .

$2 x^{- 2} y^{- 1} \cdot 6 \frac{1}{3}$

Step 5

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

$2 \frac{1}{x^{2}} y^{- 1} \cdot 6 \frac{1}{3}$

Step 6

Combine $2$ and $\frac{1}{x^{2}}$ .

$\frac{2}{x^{2}} y^{- 1} \cdot 6 \frac{1}{3}$

Step 7

Cancel the common factor of $3$ .

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Step 7.1

Factor $3$ out of $\frac{2}{x^{2}} y^{- 1} \cdot 6$ .

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

Step 7.2

Cancel the common factor.

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

Step 7.3

Rewrite the expression.

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

Step 8

Combine $\frac{2}{x^{2}}$ and $y^{- 1}$ .

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

Step 9

Combine $\frac{2 y^{- 1}}{x^{2}}$ and $2$ .

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

Step 10

Simplify the expression.

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Step 10.1

Multiply $2$ by $2$ .

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

Step 10.2

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

$\frac{4}{x^{2} y}$