Simplify ((a^5b^4)/(x^6b^3))^0

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

Step 1

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

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.

Apply the product rule to $\frac{a^{5} b}{x^{6}}$ .

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

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

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

Step 3

Simplify the numerator.

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

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

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

Multiply $5$ by $0$ .

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

Anything raised to $0$ is $1$ .

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

Anything raised to $0$ is $1$ .

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

Multiply $1$ by $1$ .

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

Step 4

Simplify the denominator.

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

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

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

Multiply $6$ by $0$ .

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

Anything raised to $0$ is $1$ .

$\frac{1}{1}$

Step 5

Divide $1$ by $1$ .

$1$