Finite Math Examples

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

Step 1

Multiply $m^{3 x + y}$ by $m^{x - 2 y}$ by adding the exponents.

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Step 1.1

Move $m^{x - 2 y}$ .

$\frac{m^{x - 2 y} m^{3 x + y} \cdot 2}{3 m^{- 2 x + 3 y}}$

Step 1.2

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

$\frac{m^{x - 2 y + 3 x + y} \cdot 2}{3 m^{- 2 x + 3 y}}$

Step 1.3

Add $x$ and $3 x$ .

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

Step 1.4

Add $- 2 y$ and $y$ .

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

Step 2

Cancel the common factor of $m^{4 x - y}$ and $m^{- 2 x + 3 y}$ .

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Step 2.1

Factor $m^{- 2 x + 3 y}$ out of $m^{4 x - y} \cdot 2$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $m^{- 2 x + 3 y}$ out of $3 m^{- 2 x + 3 y}$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

Simplify the numerator.

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Step 3.1

Simplify each term.

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Step 3.1.1

Apply the distributive property.

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

Step 3.1.2

Multiply $- 2$ by $- 1$ .

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

Step 3.1.3

Multiply $3$ by $- 1$ .

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

Step 3.2

Add $4 x$ and $2 x$ .

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

Step 3.3

Subtract $3 y$ from $- y$ .

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

Step 4

Move $2$ to the left of $m^{6 x - 4 y}$ .

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