Simplify ((ab^2)/(cd^3))^0

${(\frac{a b^{2}}{c d^{3}})}^{0}$

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

Apply the product rule to $\frac{a b^{2}}{c d^{3}}$ .

$\frac{{(a b^{2})}^{0}}{{(c d^{3})}^{0}}$

Apply the product rule to $a b^{2}$ .

$\frac{a^{0} {(b^{2})}^{0}}{{(c d^{3})}^{0}}$

Apply the product rule to $c d^{3}$ .

$\frac{a^{0} {(b^{2})}^{0}}{c^{0} {(d^{3})}^{0}}$

Simplify the numerator.

Anything raised to $0$ is $1$ .

$\frac{1 {(b^{2})}^{0}}{c^{0} {(d^{3})}^{0}}$

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

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

$\frac{1 b^{2 \cdot 0}}{c^{0} {(d^{3})}^{0}}$

Multiply $2$ by $0$ .

$\frac{1 b^{0}}{c^{0} {(d^{3})}^{0}}$

Anything raised to $0$ is $1$ .

$\frac{1 \cdot 1}{c^{0} {(d^{3})}^{0}}$

Multiply $1$ by $1$ .

$\frac{1}{c^{0} {(d^{3})}^{0}}$

Simplify the denominator.

Anything raised to $0$ is $1$ .

$\frac{1}{1 {(d^{3})}^{0}}$

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

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

$\frac{1}{1 d^{3 \cdot 0}}$

Multiply $3$ by $0$ .

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

Anything raised to $0$ is $1$ .

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

Multiply $1$ by $1$ .

$\frac{1}{1}$

Divide $1$ by $1$ .

$1$