Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

Move $z^{2}$ .

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

Step 1.2.2

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

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

Step 1.2.3

Add $2$ and $2$ .

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

Step 1.3

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

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

Step 1.4

Multiply the exponents in ${(x^{2})}^{2}$ .

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Step 1.4.1

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

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

Step 1.4.2

Multiply $2$ by $2$ .

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

Step 1.5

Combine exponents.

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Step 1.5.1

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

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

Step 1.5.2

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

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

Step 1.5.3

Add $1$ and $4$ .

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

Step 1.5.4

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

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Step 1.5.4.1

Move $y^{2}$ .

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

Step 1.5.4.2

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

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

Step 1.5.4.3

Add $2$ and $2$ .

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

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $x y z$ .

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

Step 2.2

Apply the product rule to $x y$ .

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

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $x^{5}$ and $x^{2}$ .

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Step 3.1.1

Factor $x^{2}$ out of $x^{5} y^{4} z^{4}$ .

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

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

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

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

Step 3.1.2.2

Cancel the common factor.

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

Step 3.1.2.3

Rewrite the expression.

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

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

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

Step 3.2.2.2

Cancel the common factor.

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

Step 3.2.2.3

Rewrite the expression.

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

Step 3.3

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

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Step 3.3.1

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

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

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Multiply by $1$ .

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

Step 3.3.2.2

Cancel the common factor.

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

Step 3.3.2.3

Rewrite the expression.

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

Step 3.3.2.4

Divide $x^{3} y^{2} z^{2}$ by $1$ .

$x^{3} y^{2} z^{2}$