Algebra Examples

$(x^{- 3} y^{5} z^{- 4}) \cdot (x^{6} y^{- 7} z^{- 2})$

Step 1

Multiply $x^{- 3}$ by $x^{6}$ by adding the exponents.

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Step 1.1

Move $x^{6}$ .

$x^{6} x^{- 3} y^{5} z^{- 4} \cdot (y^{- 7} z^{- 2})$

Step 1.2

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

$x^{6 - 3} y^{5} z^{- 4} \cdot (y^{- 7} z^{- 2})$

Step 1.3

Subtract $3$ from $6$ .

$x^{3} y^{5} z^{- 4} \cdot (y^{- 7} z^{- 2})$

Step 2

Multiply $y^{5}$ by $y^{- 7}$ by adding the exponents.

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Step 2.1

Move $y^{- 7}$ .

$x^{3} (y^{- 7} y^{5}) z^{- 4} \cdot z^{- 2}$

Step 2.2

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

$x^{3} y^{- 7 + 5} z^{- 4} \cdot z^{- 2}$

Step 2.3

Add $- 7$ and $5$ .

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

Step 3

Multiply $z^{- 4}$ by $z^{- 2}$ by adding the exponents.

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Step 3.1

Move $z^{- 2}$ .

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

Step 3.2

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

$x^{3} y^{- 2} z^{- 2 - 4}$

Step 3.3

Subtract $4$ from $- 2$ .

$x^{3} y^{- 2} z^{- 6}$

Step 4

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

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

Step 5

Combine $x^{3}$ and $\frac{1}{y^{2}}$ .

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

Step 6

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

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

Step 7

Combine.

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

Step 8

Multiply $x^{3}$ by $1$ .

$\frac{x^{3}}{y^{2} z^{6}}$