Precalculus Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

Multiply $2$ by $2$ .

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

Step 1.4

Combine exponents.

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Step 1.4.1

Multiply $4$ by $3$ .

$\frac{12 y^{3} y^{4}}{{(y^{3})}^{4}} \cdot y^{0}$

Step 1.4.2

Multiply $y^{3}$ by $y^{4}$ by adding the exponents.

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Step 1.4.2.1

Move $y^{4}$ .

$\frac{12 (y^{4} y^{3})}{{(y^{3})}^{4}} \cdot y^{0}$

Step 1.4.2.2

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

$\frac{12 y^{4 + 3}}{{(y^{3})}^{4}} \cdot y^{0}$

Step 1.4.2.3

Add $4$ and $3$ .

$\frac{12 y^{7}}{{(y^{3})}^{4}} \cdot y^{0}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

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

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Step 2.1.1

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

$\frac{12 y^{7}}{y^{3 \cdot 4}} \cdot y^{0}$

Step 2.1.2

Multiply $3$ by $4$ .

$\frac{12 y^{7}}{y^{12}} \cdot y^{0}$

Step 2.2

Cancel the common factor of $y^{0}$ .

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Step 2.2.1

Factor $y^{0}$ out of $y^{12}$ .

$\frac{12 y^{7}}{y^{0} y^{12}} \cdot y^{0}$

Step 2.2.2

Cancel the common factor.

$\frac{12 y^{7}}{y^{0} y^{12}} \cdot y^{0}$

Step 2.2.3

Rewrite the expression.

$\frac{12 y^{7}}{y^{12}}$

Step 2.3

Cancel the common factor of $y^{7}$ and $y^{12}$ .

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Step 2.3.1

Factor $y^{7}$ out of $12 y^{7}$ .

$\frac{y^{7} \cdot 12}{y^{12}}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $y^{7}$ out of $y^{12}$ .

$\frac{y^{7} \cdot 12}{y^{7} y^{5}}$

Step 2.3.2.2

Cancel the common factor.

$\frac{y^{7} \cdot 12}{y^{7} y^{5}}$

Step 2.3.2.3

Rewrite the expression.

$\frac{12}{y^{5}}$