Algebra Examples

$\frac{{(2 x^{3})}^{2} {(3 y^{4})}^{3}}{12 x^{4} y^{5}}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{2^{2} {(x^{3})}^{2} {(3 y^{4})}^{3}}{12 x^{4} y^{5}}$

Step 1.2

Apply the product rule to $3 y^{4}$ .

$\frac{2^{2} {(x^{3})}^{2} \cdot 3^{3} {(y^{4})}^{3}}{12 x^{4} y^{5}}$

Step 1.3

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

$\frac{4 {(x^{3})}^{2} \cdot 3^{3} {(y^{4})}^{3}}{12 x^{4} y^{5}}$

Step 1.4

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

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Step 1.4.1

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

$\frac{4 x^{3 \cdot 2} \cdot 3^{3} {(y^{4})}^{3}}{12 x^{4} y^{5}}$

Step 1.4.2

Multiply $3$ by $2$ .

$\frac{4 x^{6} \cdot 3^{3} {(y^{4})}^{3}}{12 x^{4} y^{5}}$

Step 1.5

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

$\frac{4 x^{6} \cdot 27 {(y^{4})}^{3}}{12 x^{4} y^{5}}$

Step 1.6

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

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Step 1.6.1

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

$\frac{4 x^{6} \cdot 27 y^{4 \cdot 3}}{12 x^{4} y^{5}}$

Step 1.6.2

Multiply $4$ by $3$ .

$\frac{4 x^{6} \cdot 27 y^{12}}{12 x^{4} y^{5}}$

Step 1.7

Multiply $27$ by $4$ .

$\frac{108 x^{6} y^{12}}{12 x^{4} y^{5}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $108$ and $12$ .

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Step 2.1.1

Factor $12$ out of $108 x^{6} y^{12}$ .

$\frac{12 (9 x^{6} y^{12})}{12 x^{4} y^{5}}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $12$ out of $12 x^{4} y^{5}$ .

$\frac{12 (9 x^{6} y^{12})}{12 (x^{4} y^{5})}$

Step 2.1.2.2

Cancel the common factor.

$\frac{12 (9 x^{6} y^{12})}{12 (x^{4} y^{5})}$

Step 2.1.2.3

Rewrite the expression.

$\frac{9 x^{6} y^{12}}{x^{4} y^{5}}$

Step 2.2

Cancel the common factor of $x^{6}$ and $x^{4}$ .

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Step 2.2.1

Factor $x^{4}$ out of $9 x^{6} y^{12}$ .

$\frac{x^{4} (9 x^{2} y^{12})}{x^{4} y^{5}}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $x^{4}$ out of $x^{4} y^{5}$ .

$\frac{x^{4} (9 x^{2} y^{12})}{x^{4} (y^{5})}$

Step 2.2.2.2

Cancel the common factor.

$\frac{x^{4} (9 x^{2} y^{12})}{x^{4} y^{5}}$

Step 2.2.2.3

Rewrite the expression.

$\frac{9 x^{2} y^{12}}{y^{5}}$

Step 2.3

Cancel the common factor of $y^{12}$ and $y^{5}$ .

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Step 2.3.1

Factor $y^{5}$ out of $9 x^{2} y^{12}$ .

$\frac{y^{5} (9 x^{2} y^{7})}{y^{5}}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Multiply by $1$ .

$\frac{y^{5} (9 x^{2} y^{7})}{y^{5} \cdot 1}$

Step 2.3.2.2

Cancel the common factor.

$\frac{y^{5} (9 x^{2} y^{7})}{y^{5} \cdot 1}$

Step 2.3.2.3

Rewrite the expression.

$\frac{9 x^{2} y^{7}}{1}$

Step 2.3.2.4

Divide $9 x^{2} y^{7}$ by $1$ .

$9 x^{2} y^{7}$