Finite Math Examples

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

Step 1

Move ${(x^{4} y^{- 3})}^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{x^{5} y^{2} {(x^{4} y^{- 3})}^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $x^{4} y^{- 3}$ .

$\frac{1}{x^{5} y^{2} {(x^{4})}^{2} {(y^{- 3})}^{2}}$

Step 2.2

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

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Step 2.2.1

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

$\frac{1}{x^{5} y^{2} x^{4 \cdot 2} {(y^{- 3})}^{2}}$

Step 2.2.2

Multiply $4$ by $2$ .

$\frac{1}{x^{5} y^{2} x^{8} {(y^{- 3})}^{2}}$

Step 2.3

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

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Step 2.3.1

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

$\frac{1}{x^{5} y^{2} x^{8} y^{- 3 \cdot 2}}$

Step 2.3.2

Multiply $- 3$ by $2$ .

$\frac{1}{x^{5} y^{2} x^{8} y^{- 6}}$

Step 2.4

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

$\frac{1}{x^{5} y^{2} x^{8} \frac{1}{y^{6}}}$

Step 2.5

Combine exponents.

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Step 2.5.1

Multiply $x^{5}$ by $x^{8}$ by adding the exponents.

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Step 2.5.1.1

Move $x^{8}$ .

$\frac{1}{x^{8} x^{5} y^{2} \frac{1}{y^{6}}}$

Step 2.5.1.2

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

$\frac{1}{x^{8 + 5} y^{2} \frac{1}{y^{6}}}$

Step 2.5.1.3

Add $8$ and $5$ .

$\frac{1}{x^{13} y^{2} \frac{1}{y^{6}}}$

Step 2.5.2

Combine $x^{13}$ and $\frac{1}{y^{6}}$ .

$\frac{1}{y^{2} \frac{x^{13}}{y^{6}}}$

Step 2.5.3

Combine $y^{2}$ and $\frac{x^{13}}{y^{6}}$ .

$\frac{1}{\frac{y^{2} x^{13}}{y^{6}}}$

Step 2.6

Reduce the expression $\frac{y^{2} x^{13}}{y^{6}}$ by cancelling the common factors.

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Step 2.6.1

Factor $y^{2}$ out of $y^{2} x^{13}$ .

$\frac{1}{\frac{y^{2} (x^{13})}{y^{6}}}$

Step 2.6.2

Factor $y^{2}$ out of $y^{6}$ .

$\frac{1}{\frac{y^{2} (x^{13})}{y^{2} y^{4}}}$

Step 2.6.3

Cancel the common factor.

$\frac{1}{\frac{y^{2} x^{13}}{y^{2} y^{4}}}$

Step 2.6.4

Rewrite the expression.

$\frac{1}{\frac{x^{13}}{y^{4}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{y^{4}}{x^{13}}$

Step 4

Multiply $\frac{y^{4}}{x^{13}}$ by $1$ .

$\frac{y^{4}}{x^{13}}$