Precalculus Examples

$\frac{{(6 y^{3})}^{4}}{2 y^{3}}$

Step 1

Simplify the numerator.

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Step 1.1

Apply the product rule to $6 y^{3}$ .

$\frac{6^{4} {(y^{3})}^{4}}{2 y^{3}}$

Step 1.2

Raise $6$ to the power of $4$ .

$\frac{1296 {(y^{3})}^{4}}{2 y^{3}}$

Step 1.3

Multiply the exponents in ${(y^{3})}^{4}$ .

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Step 1.3.1

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

$\frac{1296 y^{3 \cdot 4}}{2 y^{3}}$

Step 1.3.2

Multiply $3$ by $4$ .

$\frac{1296 y^{12}}{2 y^{3}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $1296$ and $2$ .

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Step 2.1.1

Factor $2$ out of $1296 y^{12}$ .

$\frac{2 (648 y^{12})}{2 y^{3}}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

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

$\frac{2 (648 y^{12})}{2 (y^{3})}$

Step 2.1.2.2

Cancel the common factor.

$\frac{2 (648 y^{12})}{2 y^{3}}$

Step 2.1.2.3

Rewrite the expression.

$\frac{648 y^{12}}{y^{3}}$

Step 2.2

Cancel the common factor of $y^{12}$ and $y^{3}$ .

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Step 2.2.1

Factor $y^{3}$ out of $648 y^{12}$ .

$\frac{y^{3} (648 y^{9})}{y^{3}}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Multiply by $1$ .

$\frac{y^{3} (648 y^{9})}{y^{3} \cdot 1}$

Step 2.2.2.2

Cancel the common factor.

$\frac{y^{3} (648 y^{9})}{y^{3} \cdot 1}$

Step 2.2.2.3

Rewrite the expression.

$\frac{648 y^{9}}{1}$

Step 2.2.2.4

Divide $648 y^{9}$ by $1$ .

$648 y^{9}$