Precalculus Examples

$\frac{{(2 x^{- 9} y^{3})}^{- 2} {(9 x^{3} y^{- 3})}^{0}}{{(2 x^{- 4} y^{- 6})}^{2}}$

Step 1

Move ${(2 x^{- 9} y^{3})}^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(2 x^{- 4} y^{- 6})}^{2} {(2 x^{- 9} y^{3})}^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $2 x^{- 4} y^{- 6}$ .

$\frac{1}{{(2 x^{- 4})}^{2} {(y^{- 6})}^{2} {(2 x^{- 9} y^{3})}^{2}}$

Step 2.2

Apply the product rule to $2 x^{- 9} y^{3}$ .

$\frac{1}{{(2 x^{- 4})}^{2} {(y^{- 6})}^{2} {(2 x^{- 9})}^{2} {(y^{3})}^{2}}$

Step 2.3

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

$\frac{1}{{(2 \frac{1}{x^{4}})}^{2} {(y^{- 6})}^{2} {(2 x^{- 9})}^{2} {(y^{3})}^{2}}$

Step 2.4

Combine $2$ and $\frac{1}{x^{4}}$ .

$\frac{1}{{(\frac{2}{x^{4}})}^{2} {(y^{- 6})}^{2} {(2 x^{- 9})}^{2} {(y^{3})}^{2}}$

Step 2.5

Apply the product rule to $\frac{2}{x^{4}}$ .

$\frac{1}{\frac{2^{2}}{{(x^{4})}^{2}} {(y^{- 6})}^{2} {(2 x^{- 9})}^{2} {(y^{3})}^{2}}$

Step 2.6

Raise $2$ to the power of $2$ .

$\frac{1}{\frac{4}{{(x^{4})}^{2}} {(y^{- 6})}^{2} {(2 x^{- 9})}^{2} {(y^{3})}^{2}}$

Step 2.7

Multiply the exponents in ${(x^{4})}^{2}$ .

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Step 2.7.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{1}{\frac{4}{x^{4 \cdot 2}} {(y^{- 6})}^{2} {(2 x^{- 9})}^{2} {(y^{3})}^{2}}$

Step 2.7.2

Multiply $4$ by $2$ .

$\frac{1}{\frac{4}{x^{8}} {(y^{- 6})}^{2} {(2 x^{- 9})}^{2} {(y^{3})}^{2}}$

Step 2.8

Multiply the exponents in ${(y^{- 6})}^{2}$ .

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Step 2.8.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{1}{\frac{4}{x^{8}} y^{- 6 \cdot 2} {(2 x^{- 9})}^{2} {(y^{3})}^{2}}$

Step 2.8.2

Multiply $- 6$ by $2$ .

$\frac{1}{\frac{4}{x^{8}} y^{- 12} {(2 x^{- 9})}^{2} {(y^{3})}^{2}}$

Step 2.9

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

$\frac{1}{\frac{4}{x^{8}} \cdot \frac{1}{y^{12}} {(2 x^{- 9})}^{2} {(y^{3})}^{2}}$

Step 2.10

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

$\frac{1}{\frac{4}{x^{8}} \cdot \frac{1}{y^{12}} {(2 \frac{1}{x^{9}})}^{2} {(y^{3})}^{2}}$

Step 2.11

Combine $2$ and $\frac{1}{x^{9}}$ .

$\frac{1}{\frac{4}{x^{8}} \cdot \frac{1}{y^{12}} {(\frac{2}{x^{9}})}^{2} {(y^{3})}^{2}}$

Step 2.12

Apply the product rule to $\frac{2}{x^{9}}$ .

$\frac{1}{\frac{4}{x^{8}} \cdot \frac{1}{y^{12}} \frac{2^{2}}{{(x^{9})}^{2}} {(y^{3})}^{2}}$

Step 2.13

Raise $2$ to the power of $2$ .

$\frac{1}{\frac{4}{x^{8}} \cdot \frac{1}{y^{12}} \frac{4}{{(x^{9})}^{2}} {(y^{3})}^{2}}$

Step 2.14

Multiply the exponents in ${(x^{9})}^{2}$ .

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Step 2.14.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{1}{\frac{4}{x^{8}} \cdot \frac{1}{y^{12}} \frac{4}{x^{9 \cdot 2}} {(y^{3})}^{2}}$

Step 2.14.2

Multiply $9$ by $2$ .

$\frac{1}{\frac{4}{x^{8}} \cdot \frac{1}{y^{12}} \frac{4}{x^{18}} {(y^{3})}^{2}}$

Step 2.15

Multiply the exponents in ${(y^{3})}^{2}$ .

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Step 2.15.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{1}{\frac{4}{x^{8}} \cdot \frac{1}{y^{12}} \frac{4}{x^{18}} y^{3 \cdot 2}}$

Step 2.15.2

Multiply $3$ by $2$ .

$\frac{1}{\frac{4}{x^{8}} \cdot \frac{1}{y^{12}} \frac{4}{x^{18}} y^{6}}$

Step 2.16

Combine exponents.

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Step 2.16.1

Multiply $\frac{4}{x^{8}}$ by $\frac{1}{y^{12}}$ .

$\frac{1}{\frac{4}{x^{8} y^{12}} \cdot \frac{4}{x^{18}} y^{6}}$

Step 2.16.2

Multiply $\frac{4}{x^{8} y^{12}}$ by $\frac{4}{x^{18}}$ .

$\frac{1}{\frac{4 \cdot 4}{x^{8} y^{12} x^{18}} y^{6}}$

Step 2.16.3

Multiply $4$ by $4$ .

$\frac{1}{\frac{16}{x^{8} y^{12} x^{18}} y^{6}}$

Step 2.16.4

Multiply $x^{8}$ by $x^{18}$ by adding the exponents.

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Step 2.16.4.1

Move $x^{18}$ .

$\frac{1}{\frac{16}{x^{18} x^{8} y^{12}} y^{6}}$

Step 2.16.4.2

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

$\frac{1}{\frac{16}{x^{18 + 8} y^{12}} y^{6}}$

Step 2.16.4.3

Add $18$ and $8$ .

$\frac{1}{\frac{16}{x^{26} y^{12}} y^{6}}$

Step 2.16.5

Combine $\frac{16}{x^{26} y^{12}}$ and $y^{6}$ .

$\frac{1}{\frac{16 y^{6}}{x^{26} y^{12}}}$

Step 2.17

Reduce the expression $\frac{16 y^{6}}{x^{26} y^{12}}$ by cancelling the common factors.

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Step 2.17.1

Factor $y^{6}$ out of $16 y^{6}$ .

$\frac{1}{\frac{y^{6} \cdot 16}{x^{26} y^{12}}}$

Step 2.17.2

Factor $y^{6}$ out of $x^{26} y^{12}$ .

$\frac{1}{\frac{y^{6} \cdot 16}{y^{6} (x^{26} y^{6})}}$

Step 2.17.3

Cancel the common factor.

$\frac{1}{\frac{y^{6} \cdot 16}{y^{6} (x^{26} y^{6})}}$

Step 2.17.4

Rewrite the expression.

$\frac{1}{\frac{16}{x^{26} y^{6}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{x^{26} y^{6}}{16}$

Step 4

Multiply $\frac{x^{26} y^{6}}{16}$ by $1$ .

$\frac{x^{26} y^{6}}{16}$