Precalculus Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Cancel the common factors.

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Step 1.2.1

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

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 2

Simplify the numerator.

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Step 2.1

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

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

Step 2.2

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

$\frac{9 {(x^{2})}^{2} y^{2}}{3}$

Step 2.3

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

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Step 2.3.1

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

$\frac{9 x^{2 \cdot 2} y^{2}}{3}$

Step 2.3.2

Multiply $2$ by $2$ .

$\frac{9 x^{4} y^{2}}{3}$

Step 3

Cancel the common factor of $9$ and $3$ .

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Step 3.1

Factor $3$ out of $9 x^{4} y^{2}$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $3$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 3.2.4

Divide $3 x^{4} y^{2}$ by $1$ .

$3 x^{4} y^{2}$