Finite Math Examples

$\frac{x^{2} y}{z} \cdot \frac{\frac{y z^{3}}{x^{4}}}{\frac{x y^{4}}{5}}$

Step 1

Combine.

$\frac{x^{2} y \frac{y z^{3}}{x^{4}}}{z \frac{x y^{4}}{5}}$

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Combine $x^{2}$ and $\frac{y z^{3}}{x^{4}}$ .

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

Step 2.2

Combine $y$ and $\frac{x^{2} (y z^{3})}{x^{4}}$ .

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

Step 3

Combine $z$ and $\frac{x y^{4}}{5}$ .

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

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

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

$\frac{\frac{x^{2} (y^{1} y) z^{3}}{x^{4}}}{\frac{z (x y^{4})}{5}}$

Step 4.2

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

$\frac{\frac{x^{2} (y^{1} y^{1}) z^{3}}{x^{4}}}{\frac{z (x y^{4})}{5}}$

Step 4.3

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

$\frac{\frac{x^{2} y^{1 + 1} z^{3}}{x^{4}}}{\frac{z (x y^{4})}{5}}$

Step 4.4

Add $1$ and $1$ .

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

Step 5

Reduce the expression $\frac{x^{2} y^{2} z^{3}}{x^{4}}$ by cancelling the common factors.

Tap for more steps...

Step 5.1

Factor $x^{2}$ out of $x^{2} y^{2} z^{3}$ .

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

Step 5.2

Factor $x^{2}$ out of $x^{4}$ .

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

Step 5.3

Cancel the common factor.

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

Step 5.4

Rewrite the expression.

$\frac{\frac{y^{2} z^{3}}{x^{2}}}{\frac{z x y^{4}}{5}}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$\frac{y^{2} z^{3}}{x^{2}} \cdot \frac{5}{z x y^{4}}$

Step 7

Combine.

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

Step 8

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

Tap for more steps...

Step 8.1

Move $x$ .

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

Step 8.2

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

Tap for more steps...

Step 8.2.1

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

$\frac{y^{2} z^{3} \cdot 5}{x^{1} x^{2} (z y^{4})}$

Step 8.2.2

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

$\frac{y^{2} z^{3} \cdot 5}{x^{1 + 2} (z y^{4})}$

Step 8.3

Add $1$ and $2$ .

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

Step 9

Cancel the common factor of $y^{2}$ and $y^{4}$ .

Tap for more steps...

Step 9.1

Factor $y^{2}$ out of $y^{2} z^{3} \cdot 5$ .

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

Step 9.2

Cancel the common factors.

Tap for more steps...

Step 9.2.1

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

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

Step 9.2.2

Cancel the common factor.

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

Step 9.2.3

Rewrite the expression.

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

Step 10

Cancel the common factor of $z^{3}$ and $z$ .

Tap for more steps...

Step 10.1

Factor $z$ out of $z^{3} \cdot 5$ .

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

Step 10.2

Cancel the common factors.

Tap for more steps...

Step 10.2.1

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

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

Step 10.2.2

Cancel the common factor.

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

Step 10.2.3

Rewrite the expression.

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

Step 11

Move $5$ to the left of $z^{2}$ .

$\frac{5 z^{2}}{x^{3} y^{2}}$