Algebra Examples

$(x^{3} y^{- 2} z) (x^{- 5} y^{- 5} z^{- 1})$

Step 1

Multiply $x^{3}$ by $x^{- 5}$ by adding the exponents.

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Step 1.1

Move $x^{- 5}$ .

$x^{- 5} x^{3} y^{- 2} z (y^{- 5} z^{- 1})$

Step 1.2

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

$x^{- 5 + 3} y^{- 2} z (y^{- 5} z^{- 1})$

Step 1.3

Add $- 5$ and $3$ .

$x^{- 2} y^{- 2} z (y^{- 5} z^{- 1})$

Step 2

Multiply $y^{- 2}$ by $y^{- 5}$ by adding the exponents.

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Step 2.1

Move $y^{- 5}$ .

$x^{- 2} (y^{- 5} y^{- 2}) z \cdot z^{- 1}$

Step 2.2

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

$x^{- 2} y^{- 5 - 2} z \cdot z^{- 1}$

Step 2.3

Subtract $2$ from $- 5$ .

$x^{- 2} y^{- 7} z \cdot z^{- 1}$

Step 3

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

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Step 3.1

Move $z^{- 1}$ .

$x^{- 2} y^{- 7} (z^{- 1} z)$

Step 3.2

Multiply $z^{- 1}$ by $z$ .

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Step 3.2.1

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

$x^{- 2} y^{- 7} (z^{- 1} z^{1})$

Step 3.2.2

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

$x^{- 2} y^{- 7} z^{- 1 + 1}$

Step 3.3

Add $- 1$ and $1$ .

$x^{- 2} y^{- 7} z^{0}$

Step 4

Simplify $x^{- 2} y^{- 7} z^{0}$ .

$x^{- 2} y^{- 7}$

Step 5

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

$\frac{1}{x^{2}} y^{- 7}$

Step 6

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

$\frac{1}{x^{2}} \cdot \frac{1}{y^{7}}$

Step 7

Combine.

$\frac{1 \cdot 1}{x^{2} y^{7}}$

Step 8

Multiply $1$ by $1$ .

$\frac{1}{x^{2} y^{7}}$