Algebra Examples

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

Step 1

Move $y^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

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

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

Step 3

Simplify the denominator.

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Step 3.1

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

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Step 3.1.1

Move $y^{4}$ .

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

Step 3.1.2

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

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

Step 3.1.3

Subtract $3$ from $4$ .

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

Step 3.2

Simplify $3 x^{2} y^{1} z^{4}$ .

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

Step 3.3

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

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Step 3.3.1

Move $z^{3}$ .

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

Step 3.3.2

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

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

Step 3.3.3

Add $3$ and $4$ .

$\frac{2 x^{4}}{3 x^{2} y z^{7}}$

Step 4

Cancel the common factor of $x^{4}$ and $x^{2}$ .

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Step 4.1

Factor $x^{2}$ out of $2 x^{4}$ .

$\frac{x^{2} (2 x^{2})}{3 x^{2} y z^{7}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $x^{2}$ out of $3 x^{2} y z^{7}$ .

$\frac{x^{2} (2 x^{2})}{x^{2} (3 y z^{7})}$

Step 4.2.2

Cancel the common factor.

$\frac{x^{2} (2 x^{2})}{x^{2} (3 y z^{7})}$

Step 4.2.3

Rewrite the expression.

$\frac{2 x^{2}}{3 y z^{7}}$