Algebra Examples

${(- \frac{3 x y^{4} z^{2}}{x^{3} y z^{4}})}^{0}$

Step 1

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

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Step 1.1

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

${(- \frac{x (3 y^{4} z^{2})}{x^{3} y z^{4}})}^{0}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

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

${(- \frac{x (3 y^{4} z^{2})}{x (x^{2} y z^{4})})}^{0}$

Step 1.2.2

Cancel the common factor.

${(- \frac{x (3 y^{4} z^{2})}{x (x^{2} y z^{4})})}^{0}$

Step 1.2.3

Rewrite the expression.

${(- \frac{3 y^{4} z^{2}}{x^{2} y z^{4}})}^{0}$

Step 2

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

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Step 2.1

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

${(- \frac{y (3 y^{3} z^{2})}{x^{2} y z^{4}})}^{0}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

${(- \frac{y (3 y^{3} z^{2})}{y (x^{2} z^{4})})}^{0}$

Step 2.2.2

Cancel the common factor.

${(- \frac{y (3 y^{3} z^{2})}{y (x^{2} z^{4})})}^{0}$

Step 2.2.3

Rewrite the expression.

${(- \frac{3 y^{3} z^{2}}{x^{2} z^{4}})}^{0}$

Step 3

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

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Step 3.1

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

${(- \frac{z^{2} (3 y^{3})}{x^{2} z^{4}})}^{0}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

${(- \frac{z^{2} (3 y^{3})}{z^{2} (x^{2} z^{2})})}^{0}$

Step 3.2.2

Cancel the common factor.

${(- \frac{z^{2} (3 y^{3})}{z^{2} (x^{2} z^{2})})}^{0}$

Step 3.2.3

Rewrite the expression.

${(- \frac{3 y^{3}}{x^{2} z^{2}})}^{0}$

Step 4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 4.1

Apply the product rule to $- \frac{3 y^{3}}{x^{2} z^{2}}$ .

${(- 1)}^{0} {(\frac{3 y^{3}}{x^{2} z^{2}})}^{0}$

Step 4.2

Apply the product rule to $\frac{3 y^{3}}{x^{2} z^{2}}$ .

${(- 1)}^{0} \frac{{(3 y^{3})}^{0}}{{(x^{2} z^{2})}^{0}}$

Step 4.3

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

${(- 1)}^{0} \frac{3^{0} {(y^{3})}^{0}}{{(x^{2} z^{2})}^{0}}$

Step 4.4

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

${(- 1)}^{0} \frac{3^{0} {(y^{3})}^{0}}{{(x^{2})}^{0} {(z^{2})}^{0}}$

Step 5

Simplify the expression.

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Step 5.1

Anything raised to $0$ is $1$ .

$1 \frac{3^{0} {(y^{3})}^{0}}{{(x^{2})}^{0} {(z^{2})}^{0}}$

Step 5.2

Multiply $\frac{3^{0} {(y^{3})}^{0}}{{(x^{2})}^{0} {(z^{2})}^{0}}$ by $1$ .

$\frac{3^{0} {(y^{3})}^{0}}{{(x^{2})}^{0} {(z^{2})}^{0}}$

Step 6

Simplify the numerator.

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Step 6.1

Anything raised to $0$ is $1$ .

$\frac{1 {(y^{3})}^{0}}{{(x^{2})}^{0} {(z^{2})}^{0}}$

Step 6.2

Multiply the exponents in ${(y^{3})}^{0}$ .

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Step 6.2.1

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

$\frac{1 y^{3 \cdot 0}}{{(x^{2})}^{0} {(z^{2})}^{0}}$

Step 6.2.2

Multiply $3$ by $0$ .

$\frac{1 y^{0}}{{(x^{2})}^{0} {(z^{2})}^{0}}$

Step 6.3

Anything raised to $0$ is $1$ .

$\frac{1 \cdot 1}{{(x^{2})}^{0} {(z^{2})}^{0}}$

Step 6.4

Multiply $1$ by $1$ .

$\frac{1}{{(x^{2})}^{0} {(z^{2})}^{0}}$

Step 7

Simplify the denominator.

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Step 7.1

Multiply the exponents in ${(x^{2})}^{0}$ .

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Step 7.1.1

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

$\frac{1}{x^{2 \cdot 0} {(z^{2})}^{0}}$

Step 7.1.2

Multiply $2$ by $0$ .

$\frac{1}{x^{0} {(z^{2})}^{0}}$

Step 7.2

Anything raised to $0$ is $1$ .

$\frac{1}{1 {(z^{2})}^{0}}$

Step 7.3

Multiply the exponents in ${(z^{2})}^{0}$ .

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Step 7.3.1

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

$\frac{1}{1 z^{2 \cdot 0}}$

Step 7.3.2

Multiply $2$ by $0$ .

$\frac{1}{1 z^{0}}$

Step 7.4

Anything raised to $0$ is $1$ .

$\frac{1}{1 \cdot 1}$

Step 7.5

Multiply $1$ by $1$ .

$\frac{1}{1}$

Step 8

Divide $1$ by $1$ .

$1$