Finite Math Examples

$\frac{{(2 x^{3} y^{4})}^{3} (8 x^{10} y)}{4 x^{12} y^{10}}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Cancel the common factor of $8$ and $4$ .

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Step 1.1.1

Factor $4$ out of ${(2 x^{3} y^{4})}^{3} (8 x^{10} y)$ .

$\frac{4 ({(2 x^{3} y^{4})}^{3} (2 x^{10} y))}{4 x^{12} y^{10}}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $4$ out of $4 x^{12} y^{10}$ .

$\frac{4 ({(2 x^{3} y^{4})}^{3} (2 x^{10} y))}{4 (x^{12} y^{10})}$

Step 1.1.2.2

Cancel the common factor.

$\frac{4 ({(2 x^{3} y^{4})}^{3} (2 x^{10} y))}{4 (x^{12} y^{10})}$

Step 1.1.2.3

Rewrite the expression.

$\frac{{(2 x^{3} y^{4})}^{3} (2 x^{10} y)}{x^{12} y^{10}}$

Step 1.2

Cancel the common factor of $x^{10}$ and $x^{12}$ .

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Step 1.2.1

Factor $x^{10}$ out of ${(2 x^{3} y^{4})}^{3} (2 x^{10} y)$ .

$\frac{x^{10} ({(2 x^{3} y^{4})}^{3} (2 y))}{x^{12} y^{10}}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $x^{10}$ out of $x^{12} y^{10}$ .

$\frac{x^{10} ({(2 x^{3} y^{4})}^{3} (2 y))}{x^{10} (x^{2} y^{10})}$

Step 1.2.2.2

Cancel the common factor.

$\frac{x^{10} ({(2 x^{3} y^{4})}^{3} (2 y))}{x^{10} (x^{2} y^{10})}$

Step 1.2.2.3

Rewrite the expression.

$\frac{{(2 x^{3} y^{4})}^{3} (2 y)}{x^{2} y^{10}}$

Step 1.3

Cancel the common factor of $y$ and $y^{10}$ .

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Step 1.3.1

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

$\frac{y ({(2 x^{3} y^{4})}^{3} \cdot (2))}{x^{2} y^{10}}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $y$ out of $x^{2} y^{10}$ .

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

Step 1.3.2.2

Cancel the common factor.

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

Step 1.3.2.3

Rewrite the expression.

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

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $2 x^{3} y^{4}$ .

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

Step 2.2

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

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

Step 2.3

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

$\frac{8 {(x^{3})}^{3} {(y^{4})}^{3} \cdot 2}{x^{2} y^{9}}$

Step 2.4

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

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Step 2.4.1

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

$\frac{8 x^{3 \cdot 3} {(y^{4})}^{3} \cdot 2}{x^{2} y^{9}}$

Step 2.4.2

Multiply $3$ by $3$ .

$\frac{8 x^{9} {(y^{4})}^{3} \cdot 2}{x^{2} y^{9}}$

Step 2.5

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

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Step 2.5.1

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

$\frac{8 x^{9} y^{4 \cdot 3} \cdot 2}{x^{2} y^{9}}$

Step 2.5.2

Multiply $4$ by $3$ .

$\frac{8 x^{9} y^{12} \cdot 2}{x^{2} y^{9}}$

Step 2.6

Multiply $2$ by $8$ .

$\frac{16 x^{9} y^{12}}{x^{2} y^{9}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $x^{9}$ and $x^{2}$ .

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Step 3.1.1

Factor $x^{2}$ out of $16 x^{9} y^{12}$ .

$\frac{x^{2} (16 x^{7} y^{12})}{x^{2} y^{9}}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

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

$\frac{x^{2} (16 x^{7} y^{12})}{x^{2} (y^{9})}$

Step 3.1.2.2

Cancel the common factor.

$\frac{x^{2} (16 x^{7} y^{12})}{x^{2} y^{9}}$

Step 3.1.2.3

Rewrite the expression.

$\frac{16 x^{7} y^{12}}{y^{9}}$

Step 3.2

Cancel the common factor of $y^{12}$ and $y^{9}$ .

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Step 3.2.1

Factor $y^{9}$ out of $16 x^{7} y^{12}$ .

$\frac{y^{9} (16 x^{7} y^{3})}{y^{9}}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Multiply by $1$ .

$\frac{y^{9} (16 x^{7} y^{3})}{y^{9} \cdot 1}$

Step 3.2.2.2

Cancel the common factor.

$\frac{y^{9} (16 x^{7} y^{3})}{y^{9} \cdot 1}$

Step 3.2.2.3

Rewrite the expression.

$\frac{16 x^{7} y^{3}}{1}$

Step 3.2.2.4

Divide $16 x^{7} y^{3}$ by $1$ .

$16 x^{7} y^{3}$