Pre-Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Move $x^{2}$ .

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

Step 2.2

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

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

Step 2.3

Add $2$ and $2$ .

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

Step 3

Move $y^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 4

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

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

Step 5

Simplify the numerator.

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Step 5.1

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

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Step 5.1.1

Move $y^{3}$ .

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

Step 5.1.2

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

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Step 5.1.2.1

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

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

Step 5.1.2.2

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

$- \frac{3 y^{3 + 1} z^{2} z^{2}}{3 x^{4}}$

Step 5.1.3

Add $3$ and $1$ .

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

Step 5.2

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

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Step 5.2.1

Move $z^{2}$ .

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

Step 5.2.2

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

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

Step 5.2.3

Add $2$ and $2$ .

$- \frac{3 y^{4} z^{4}}{3 x^{4}}$

Step 6

Cancel the common factor of $3$ .

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Step 6.1

Cancel the common factor.

$- \frac{3 y^{4} z^{4}}{3 x^{4}}$

Step 6.2

Rewrite the expression.

$- \frac{y^{4} z^{4}}{x^{4}}$