Algebra Examples

$\frac{{(x^{2} y^{2} z^{2})}^{5}}{{(x^{3} y^{3} z^{3})}^{7}}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{{(x^{2} y^{2})}^{5} {(z^{2})}^{5}}{{(x^{3} y^{3} z^{3})}^{7}}$

Step 1.2

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

$\frac{{(x^{2})}^{5} {(y^{2})}^{5} {(z^{2})}^{5}}{{(x^{3} y^{3} z^{3})}^{7}}$

Step 1.3

Multiply the exponents in ${(x^{2})}^{5}$ .

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Step 1.3.1

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

$\frac{x^{2 \cdot 5} {(y^{2})}^{5} {(z^{2})}^{5}}{{(x^{3} y^{3} z^{3})}^{7}}$

Step 1.3.2

Multiply $2$ by $5$ .

$\frac{x^{10} {(y^{2})}^{5} {(z^{2})}^{5}}{{(x^{3} y^{3} z^{3})}^{7}}$

Step 1.4

Multiply the exponents in ${(y^{2})}^{5}$ .

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Step 1.4.1

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

$\frac{x^{10} y^{2 \cdot 5} {(z^{2})}^{5}}{{(x^{3} y^{3} z^{3})}^{7}}$

Step 1.4.2

Multiply $2$ by $5$ .

$\frac{x^{10} y^{10} {(z^{2})}^{5}}{{(x^{3} y^{3} z^{3})}^{7}}$

Step 1.5

Multiply the exponents in ${(z^{2})}^{5}$ .

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Step 1.5.1

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

$\frac{x^{10} y^{10} z^{2 \cdot 5}}{{(x^{3} y^{3} z^{3})}^{7}}$

Step 1.5.2

Multiply $2$ by $5$ .

$\frac{x^{10} y^{10} z^{10}}{{(x^{3} y^{3} z^{3})}^{7}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $x^{3} y^{3} z^{3}$ .

$\frac{x^{10} y^{10} z^{10}}{{(x^{3} y^{3})}^{7} {(z^{3})}^{7}}$

Step 2.2

Apply the product rule to $x^{3} y^{3}$ .

$\frac{x^{10} y^{10} z^{10}}{{(x^{3})}^{7} {(y^{3})}^{7} {(z^{3})}^{7}}$

Step 2.3

Multiply the exponents in ${(x^{3})}^{7}$ .

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Step 2.3.1

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

$\frac{x^{10} y^{10} z^{10}}{x^{3 \cdot 7} {(y^{3})}^{7} {(z^{3})}^{7}}$

Step 2.3.2

Multiply $3$ by $7$ .

$\frac{x^{10} y^{10} z^{10}}{x^{21} {(y^{3})}^{7} {(z^{3})}^{7}}$

Step 2.4

Multiply the exponents in ${(y^{3})}^{7}$ .

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Step 2.4.1

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

$\frac{x^{10} y^{10} z^{10}}{x^{21} y^{3 \cdot 7} {(z^{3})}^{7}}$

Step 2.4.2

Multiply $3$ by $7$ .

$\frac{x^{10} y^{10} z^{10}}{x^{21} y^{21} {(z^{3})}^{7}}$

Step 2.5

Multiply the exponents in ${(z^{3})}^{7}$ .

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Step 2.5.1

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

$\frac{x^{10} y^{10} z^{10}}{x^{21} y^{21} z^{3 \cdot 7}}$

Step 2.5.2

Multiply $3$ by $7$ .

$\frac{x^{10} y^{10} z^{10}}{x^{21} y^{21} z^{21}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $x^{10}$ and $x^{21}$ .

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Step 3.1.1

Factor $x^{10}$ out of $x^{10} y^{10} z^{10}$ .

$\frac{x^{10} (y^{10} z^{10})}{x^{21} y^{21} z^{21}}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $x^{10}$ out of $x^{21} y^{21} z^{21}$ .

$\frac{x^{10} (y^{10} z^{10})}{x^{10} (x^{11} y^{21} z^{21})}$

Step 3.1.2.2

Cancel the common factor.

$\frac{x^{10} (y^{10} z^{10})}{x^{10} (x^{11} y^{21} z^{21})}$

Step 3.1.2.3

Rewrite the expression.

$\frac{y^{10} z^{10}}{x^{11} y^{21} z^{21}}$

Step 3.2

Cancel the common factor of $y^{10}$ and $y^{21}$ .

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Step 3.2.1

Factor $y^{10}$ out of $y^{10} z^{10}$ .

$\frac{y^{10} (z^{10})}{x^{11} y^{21} z^{21}}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $y^{10}$ out of $x^{11} y^{21} z^{21}$ .

$\frac{y^{10} (z^{10})}{y^{10} (x^{11} y^{11} z^{21})}$

Step 3.2.2.2

Cancel the common factor.

$\frac{y^{10} z^{10}}{y^{10} (x^{11} y^{11} z^{21})}$

Step 3.2.2.3

Rewrite the expression.

$\frac{z^{10}}{x^{11} y^{11} z^{21}}$

Step 3.3

Cancel the common factor of $z^{10}$ and $z^{21}$ .

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Step 3.3.1

Multiply by $1$ .

$\frac{z^{10} \cdot 1}{x^{11} y^{11} z^{21}}$

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Factor $z^{10}$ out of $x^{11} y^{11} z^{21}$ .

$\frac{z^{10} \cdot 1}{z^{10} (x^{11} y^{11} z^{11})}$

Step 3.3.2.2

Cancel the common factor.

$\frac{z^{10} \cdot 1}{z^{10} (x^{11} y^{11} z^{11})}$

Step 3.3.2.3

Rewrite the expression.

$\frac{1}{x^{11} y^{11} z^{11}}$