Finite Math Examples

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

Step 1

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

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Step 1.1

Move $x^{3}$ .

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

Step 1.2

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

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

Step 1.3

Add $3$ and $4$ .

$\frac{3 x^{7} y (4 y^{2})}{2 x y^{- 1}}$

Step 2

Multiply $y$ by $y^{2}$ by adding the exponents.

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Step 2.1

Move $y^{2}$ .

$\frac{3 x^{7} (y^{2} y) \cdot 4}{2 x y^{- 1}}$

Step 2.2

Multiply $y^{2}$ by $y$ .

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Step 2.2.1

Raise $y$ to the power of $1$ .

$\frac{3 x^{7} (y^{2} y^{1}) \cdot 4}{2 x y^{- 1}}$

Step 2.2.2

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

$\frac{3 x^{7} y^{2 + 1} \cdot 4}{2 x y^{- 1}}$

Step 2.3

Add $2$ and $1$ .

$\frac{3 x^{7} y^{3} \cdot 4}{2 x y^{- 1}}$

Step 3

Move $y^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{3 x^{7} y^{3} \cdot 4 y}{2 x}$

Step 4

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

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Step 4.1

Move $y$ .

$\frac{3 x^{7} (y \cdot y^{3}) \cdot 4}{2 x}$

Step 4.2

Multiply $y$ by $y^{3}$ .

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Step 4.2.1

Raise $y$ to the power of $1$ .

$\frac{3 x^{7} (y^{1} y^{3}) \cdot 4}{2 x}$

Step 4.2.2

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

$\frac{3 x^{7} y^{1 + 3} \cdot 4}{2 x}$

Step 4.3

Add $1$ and $3$ .

$\frac{3 x^{7} y^{4} \cdot 4}{2 x}$

Step 5

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

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Step 5.1

Factor $x$ out of $3 x^{7} y^{4} \cdot 4$ .

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $x$ out of $2 x$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

$\frac{3 x^{6} y^{4} \cdot 4}{2}$

Step 6

Cancel the common factor of $4$ and $2$ .

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Step 6.1

Factor $2$ out of $3 x^{6} y^{4} \cdot 4$ .

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $2$ .

$\frac{2 (3 x^{6} y^{4} \cdot 2)}{2 (1)}$

Step 6.2.2

Cancel the common factor.

$\frac{2 (3 x^{6} y^{4} \cdot 2)}{2 \cdot 1}$

Step 6.2.3

Rewrite the expression.

$\frac{3 x^{6} y^{4} \cdot 2}{1}$

Step 6.2.4

Divide $3 x^{6} y^{4} \cdot 2$ by $1$ .

$3 x^{6} y^{4} \cdot 2$

Step 7

Multiply $2$ by $3$ .

$6 x^{6} y^{4}$