Algebra Examples

${(\frac{a^{5} b^{4}}{x^{6} b^{3}})}^{0}$

Step 1

Cancel the common factor of $b^{4}$ and $b^{3}$ .

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Step 1.1

Factor $b^{3}$ out of $a^{5} b^{4}$ .

${(\frac{b^{3} (a^{5} b)}{x^{6} b^{3}})}^{0}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $b^{3}$ out of $x^{6} b^{3}$ .

${(\frac{b^{3} (a^{5} b)}{b^{3} x^{6}})}^{0}$

Step 1.2.2

Cancel the common factor.

${(\frac{b^{3} (a^{5} b)}{b^{3} x^{6}})}^{0}$

Step 1.2.3

Rewrite the expression.

${(\frac{a^{5} b}{x^{6}})}^{0}$

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 $\frac{a^{5} b}{x^{6}}$ .

$\frac{{(a^{5} b)}^{0}}{{(x^{6})}^{0}}$

Step 2.2

Apply the product rule to $a^{5} b$ .

$\frac{{(a^{5})}^{0} b^{0}}{{(x^{6})}^{0}}$

Step 3

Simplify the numerator.

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Step 3.1

Multiply the exponents in ${(a^{5})}^{0}$ .

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Step 3.1.1

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

$\frac{a^{5 \cdot 0} b^{0}}{{(x^{6})}^{0}}$

Step 3.1.2

Multiply $5$ by $0$ .

$\frac{a^{0} b^{0}}{{(x^{6})}^{0}}$

Step 3.2

Anything raised to $0$ is $1$ .

$\frac{1 b^{0}}{{(x^{6})}^{0}}$

Step 3.3

Anything raised to $0$ is $1$ .

$\frac{1 \cdot 1}{{(x^{6})}^{0}}$

Step 3.4

Multiply $1$ by $1$ .

$\frac{1}{{(x^{6})}^{0}}$

Step 4

Simplify the denominator.

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Step 4.1

Multiply the exponents in ${(x^{6})}^{0}$ .

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Step 4.1.1

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

$\frac{1}{x^{6 \cdot 0}}$

Step 4.1.2

Multiply $6$ by $0$ .

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

Step 4.2

Anything raised to $0$ is $1$ .

$\frac{1}{1}$

Step 5

Divide $1$ by $1$ .

$1$