Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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Step 3.1

Move $x^{2}$ .

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

Step 3.2

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

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

Step 3.3

Add $2$ and $2$ .

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

Step 4

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

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

Step 5

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 5.1

Apply the product rule to $\frac{2 x^{4} y}{3}$ .

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

Step 5.2

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

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

Step 5.3

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

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

Step 6

Simplify the numerator.

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Step 6.1

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

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

Step 6.2

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

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Step 6.2.1

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

$\frac{4 x^{4 \cdot 2} y^{2}}{3^{2}}$

Step 6.2.2

Multiply $4$ by $2$ .

$\frac{4 x^{8} y^{2}}{3^{2}}$

Step 7

Raise $3$ to the power of $2$ .

$\frac{4 x^{8} y^{2}}{9}$