Algebra Examples

${(\frac{4 x y^{2}}{5 x^{3}})}^{0}$

Step 1

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

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Step 1.1

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

${(\frac{x (4 y^{2})}{5 x^{3}})}^{0}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $x$ out of $5 x^{3}$ .

${(\frac{x (4 y^{2})}{x (5 x^{2})})}^{0}$

Step 1.2.2

Cancel the common factor.

${(\frac{x (4 y^{2})}{x (5 x^{2})})}^{0}$

Step 1.2.3

Rewrite the expression.

${(\frac{4 y^{2}}{5 x^{2}})}^{0}$

Step 2

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

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Step 2.1

Apply the product rule to $\frac{4 y^{2}}{5 x^{2}}$ .

$\frac{{(4 y^{2})}^{0}}{{(5 x^{2})}^{0}}$

Step 2.2

Apply the product rule to $4 y^{2}$ .

$\frac{4^{0} {(y^{2})}^{0}}{{(5 x^{2})}^{0}}$

Step 2.3

Apply the product rule to $5 x^{2}$ .

$\frac{4^{0} {(y^{2})}^{0}}{5^{0} {(x^{2})}^{0}}$

Step 3

Simplify the numerator.

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Step 3.1

Anything raised to $0$ is $1$ .

$\frac{1 {(y^{2})}^{0}}{5^{0} {(x^{2})}^{0}}$

Step 3.2

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

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Step 3.2.1

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

$\frac{1 y^{2 \cdot 0}}{5^{0} {(x^{2})}^{0}}$

Step 3.2.2

Multiply $2$ by $0$ .

$\frac{1 y^{0}}{5^{0} {(x^{2})}^{0}}$

Step 3.3

Anything raised to $0$ is $1$ .

$\frac{1 \cdot 1}{5^{0} {(x^{2})}^{0}}$

Step 3.4

Multiply $1$ by $1$ .

$\frac{1}{5^{0} {(x^{2})}^{0}}$

Step 4

Simplify the denominator.

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Step 4.1

Anything raised to $0$ is $1$ .

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

Step 4.2

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

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Step 4.2.1

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

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

Step 4.2.2

Multiply $2$ by $0$ .

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

Step 4.3

Anything raised to $0$ is $1$ .

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

Step 4.4

Multiply $1$ by $1$ .

$\frac{1}{1}$

Step 5

Divide $1$ by $1$ .

$1$