Finite Math Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Move $y^{3}$ .

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

Step 2.2

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

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

Step 2.3

Add $3$ and $4$ .

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

Step 3

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

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

Step 4

Simplify the numerator.

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Step 4.1

Multiply $x^{- 2}$ by $x^{3}$ by adding the exponents.

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Step 4.1.1

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

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

Step 4.1.2

Add $- 2$ and $3$ .

${(\frac{x^{1}}{y^{7}})}^{- 2}$

Step 4.2

Simplify $x^{1}$ .

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

Step 5

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Step 6

Apply the product rule to $\frac{y^{7}}{x}$ .

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

Step 7

Multiply the exponents in ${(y^{7})}^{2}$ .

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Step 7.1

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

$\frac{y^{7 \cdot 2}}{x^{2}}$

Step 7.2

Multiply $7$ by $2$ .

$\frac{y^{14}}{x^{2}}$