Algebra Examples

${(\frac{y x^{- 3} \cdot 2 x^{0} y^{3}}{2 x y^{3}})}^{2}$

Step 1

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

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Step 1.1

Move $y^{3}$ .

${(\frac{y^{3} y x^{- 3} \cdot (2 x^{0})}{2 x y^{3}})}^{2}$

Step 1.2

Multiply $y^{3}$ by $y$ .

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Step 1.2.1

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

${(\frac{y^{3} y^{1} x^{- 3} \cdot (2 x^{0})}{2 x y^{3}})}^{2}$

Step 1.2.2

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

${(\frac{y^{3 + 1} x^{- 3} \cdot (2 x^{0})}{2 x y^{3}})}^{2}$

Step 1.3

Add $3$ and $1$ .

${(\frac{y^{4} x^{- 3} \cdot (2 x^{0})}{2 x y^{3}})}^{2}$

Step 2

Simplify $y^{4} x^{- 3} \cdot (2 x^{0})$ .

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

Step 3

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

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

Step 4

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

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Step 4.1

Move $x^{3}$ .

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

Step 4.2

Multiply $x^{3}$ by $x$ .

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Step 4.2.1

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

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

Step 4.2.2

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

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

Step 4.3

Add $3$ and $1$ .

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

Step 5

Cancel the common factor of $y^{4}$ and $y^{3}$ .

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Step 5.1

Factor $y^{3}$ out of $y^{4} \cdot 2$ .

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

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

Step 7

Apply basic rules of exponents.

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Step 7.1

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

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

Step 7.2

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

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Step 7.2.1

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

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

Step 7.2.2

Multiply $4$ by $2$ .

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