Simplify ((2a^4b^3)/(c^6))^0

${(\frac{2 a^{4} b^{3}}{c^{6}})}^{0}$

Step 1

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

Apply the product rule to $\frac{2 a^{4} b^{3}}{c^{6}}$ .

$\frac{{(2 a^{4} b^{3})}^{0}}{{(c^{6})}^{0}}$

Apply the product rule to $2 a^{4} b^{3}$ .

$\frac{{(2 a^{4})}^{0} {(b^{3})}^{0}}{{(c^{6})}^{0}}$

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

$\frac{2^{0} {(a^{4})}^{0} {(b^{3})}^{0}}{{(c^{6})}^{0}}$

Step 2

Simplify the numerator.

Anything raised to $0$ is $1$ .

$\frac{1 {(a^{4})}^{0} {(b^{3})}^{0}}{{(c^{6})}^{0}}$

Multiply the exponents in ${(a^{4})}^{0}$ .

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

$\frac{1 a^{4 \cdot 0} {(b^{3})}^{0}}{{(c^{6})}^{0}}$

Multiply $4$ by $0$ .

$\frac{1 a^{0} {(b^{3})}^{0}}{{(c^{6})}^{0}}$

Anything raised to $0$ is $1$ .

$\frac{1 \cdot 1 {(b^{3})}^{0}}{{(c^{6})}^{0}}$

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

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

$\frac{1 \cdot 1 b^{3 \cdot 0}}{{(c^{6})}^{0}}$

Multiply $3$ by $0$ .

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

Anything raised to $0$ is $1$ .

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

Combine exponents.

Multiply $1$ by $1$ .

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

Multiply $1$ by $1$ .

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

Step 3

Simplify the denominator.

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

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

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

Multiply $6$ by $0$ .

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

Anything raised to $0$ is $1$ .

$\frac{1}{1}$

Step 4

Divide $1$ by $1$ .

$1$