Precalculus Examples

$\frac{27 x^{- 5} y^{12}}{18 x^{5} y^{- 3}}$

Step 1

Move $x^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{27 y^{12}}{18 x^{5} y^{- 3} x^{5}}$

Step 2

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

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Step 2.1

Move $x^{5}$ .

$\frac{27 y^{12}}{18 (x^{5} x^{5}) y^{- 3}}$

Step 2.2

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

$\frac{27 y^{12}}{18 x^{5 + 5} y^{- 3}}$

Step 2.3

Add $5$ and $5$ .

$\frac{27 y^{12}}{18 x^{10} y^{- 3}}$

Step 3

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

$\frac{27 y^{12} y^{3}}{18 x^{10}}$

Step 4

Multiply $y^{12}$ by $y^{3}$ by adding the exponents.

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Step 4.1

Move $y^{3}$ .

$\frac{27 (y^{3} y^{12})}{18 x^{10}}$

Step 4.2

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

$\frac{27 y^{3 + 12}}{18 x^{10}}$

Step 4.3

Add $3$ and $12$ .

$\frac{27 y^{15}}{18 x^{10}}$

Step 5

Cancel the common factor of $27$ and $18$ .

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Step 5.1

Factor $9$ out of $27 y^{15}$ .

$\frac{9 (3 y^{15})}{18 x^{10}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $9$ out of $18 x^{10}$ .

$\frac{9 (3 y^{15})}{9 (2 x^{10})}$

Step 5.2.2

Cancel the common factor.

$\frac{9 (3 y^{15})}{9 (2 x^{10})}$

Step 5.2.3

Rewrite the expression.

$\frac{3 y^{15}}{2 x^{10}}$