Pre-Algebra Examples

$\frac{5 x^{2} y^{4} z^{- 2}}{15 x^{- 4} y^{- 3} z^{- 2}}$

Step 1

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

$\frac{5 x^{2} y^{4} z^{- 2} x^{4}}{15 y^{- 3} z^{- 2}}$

Step 2

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

$\frac{5 x^{2} y^{4} z^{- 2} x^{4} y^{3}}{15 z^{- 2}}$

Step 3

Simplify the numerator.

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Step 3.1

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

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Step 3.1.1

Move $x^{4}$ .

$\frac{5 (x^{4} x^{2}) y^{4} z^{- 2} y^{3}}{15 z^{- 2}}$

Step 3.1.2

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

$\frac{5 x^{4 + 2} y^{4} z^{- 2} y^{3}}{15 z^{- 2}}$

Step 3.1.3

Add $4$ and $2$ .

$\frac{5 x^{6} y^{4} z^{- 2} y^{3}}{15 z^{- 2}}$

Step 3.2

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

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Step 3.2.1

Move $y^{3}$ .

$\frac{5 x^{6} (y^{3} y^{4}) z^{- 2}}{15 z^{- 2}}$

Step 3.2.2

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

$\frac{5 x^{6} y^{3 + 4} z^{- 2}}{15 z^{- 2}}$

Step 3.2.3

Add $3$ and $4$ .

$\frac{5 x^{6} y^{7} z^{- 2}}{15 z^{- 2}}$

Step 4

Cancel the common factor of $5$ and $15$ .

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Step 4.1

Factor $5$ out of $5 x^{6} y^{7} z^{- 2}$ .

$\frac{5 (x^{6} y^{7} z^{- 2})}{15 z^{- 2}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $5$ out of $15 z^{- 2}$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

$\frac{x^{6} y^{7} z^{- 2}}{3 z^{- 2}}$

Step 5

Cancel the common factor of $z^{- 2}$ .

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Step 5.1

Cancel the common factor.

$\frac{x^{6} y^{7} z^{- 2}}{3 z^{- 2}}$

Step 5.2

Rewrite the expression.

$\frac{x^{6} y^{7}}{3}$