Algebra Examples

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

Step 1

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

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

Step 2

Cancel the common factor of $- 4$ and $8$ .

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Step 2.1

Factor $4$ out of $- 4 x^{3} y^{2}$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $4$ out of $8$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

Move the negative in front of the fraction.

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

Step 4

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

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

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

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

Step 5

Simplify the expression.

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Step 5.1

Raise $- 1$ to the power of $2$ .

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

Step 5.2

Multiply $\frac{{(x^{3})}^{2} {(y^{2})}^{2}}{2^{2}}$ by $1$ .

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

Step 6

Simplify the numerator.

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Step 6.1

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

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Step 6.1.1

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

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

Step 6.1.2

Multiply $3$ by $2$ .

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

Step 6.2

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

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Step 6.2.1

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

$\frac{x^{6} y^{2 \cdot 2}}{2^{2}}$

Step 6.2.2

Multiply $2$ by $2$ .

$\frac{x^{6} y^{4}}{2^{2}}$

Step 7

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

$\frac{x^{6} y^{4}}{4}$