Pre-Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Move $x^{4}$ .

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

Step 2.2

Multiply $x^{4}$ by $x$ .

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Step 2.2.1

Raise $x$ to the power of $1$ .

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

Step 2.2.2

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

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

Step 2.3

Add $4$ and $1$ .

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

Step 3

Cancel the common factor of $y^{3}$ and $y^{2}$ .

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $y^{2}$ out of $3 x^{5} y^{2}$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

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

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

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 $\frac{3 x^{5}}{2 y}$ .

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

Step 5.2

Apply the product rule to $3 x^{5}$ .

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

Step 5.3

Apply the product rule to $2 y$ .

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

Step 6

Simplify the numerator.

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Step 6.1

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

$\frac{9 {(x^{5})}^{2}}{2^{2} y^{2}}$

Step 6.2

Multiply the exponents in ${(x^{5})}^{2}$ .

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Step 6.2.1

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

$\frac{9 x^{5 \cdot 2}}{2^{2} y^{2}}$

Step 6.2.2

Multiply $5$ by $2$ .

$\frac{9 x^{10}}{2^{2} y^{2}}$

Step 7

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

$\frac{9 x^{10}}{4 y^{2}}$