Algebra Examples

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Multiply the numerator by the reciprocal of the denominator.

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

Step 3

Combine.

$x^{2} y \frac{x y^{2} \cdot 1}{z^{2} z^{2}}$

Step 4

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

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Step 4.1

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

$x^{2} y \frac{x y^{2} \cdot 1}{z^{2 + 2}}$

Step 4.2

Add $2$ and $2$ .

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

Step 5

Multiply $x y^{2}$ by $1$ .

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

Step 6

Multiply $x^{2} y \frac{x y^{2}}{z^{4}}$ .

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Step 6.1

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

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

Step 6.2

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

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Step 6.2.1

Move $x$ .

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

Step 6.2.2

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

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Step 6.2.2.1

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

$y \frac{x^{1} x^{2} y^{2}}{z^{4}}$

Step 6.2.2.2

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

$y \frac{x^{1 + 2} y^{2}}{z^{4}}$

Step 6.2.3

Add $1$ and $2$ .

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

Step 6.3

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

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

Step 6.4

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

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

Step 6.5

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

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

Step 6.6

Add $1$ and $2$ .

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