Algebra Examples

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

Step 1

Move $x^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

Simplify the numerator.

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Step 2.1

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

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Step 2.1.1

Move $x^{4}$ .

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

Step 2.1.2

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

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

Step 2.1.3

Subtract $3$ from $4$ .

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

Step 2.2

Simplify $2 x^{1} y^{4}$ .

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

Step 3

Cancel the common factor of $y^{4}$ and $y^{2}$ .

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Step 3.1

Factor $y^{2}$ out of $2 x y^{4}$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $y^{2}$ out of $3 y^{2}$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

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

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

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 $\frac{3}{2 x y^{2}}$ .

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

Step 5.2

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

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

Step 5.3

Apply the product rule to $2 x$ .

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

Step 6

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

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

Step 7

Simplify the denominator.

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Step 7.1

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

$\frac{9}{4 x^{2} {(y^{2})}^{2}}$

Step 7.2

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

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Step 7.2.1

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

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

Step 7.2.2

Multiply $2$ by $2$ .

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