Simplify ((36257x^5x^-4)/(z^8))^0

${(\frac{36257 x^{5} x^{- 4}}{z^{8}})}^{0}$

Step 1

Multiply $x^{5}$ by $x^{- 4}$ by adding the exponents.

Move $x^{- 4}$ .

${(\frac{36257 (x^{- 4} x^{5})}{z^{8}})}^{0}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{36257 x^{- 4 + 5}}{z^{8}})}^{0}$

Add $- 4$ and $5$ .

${(\frac{36257 x^{1}}{z^{8}})}^{0}$

Step 2

Simplify $36257 x^{1}$ .

${(\frac{36257 x}{z^{8}})}^{0}$

Step 3

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

Apply the product rule to $\frac{36257 x}{z^{8}}$ .

$\frac{{(36257 x)}^{0}}{{(z^{8})}^{0}}$

Apply the product rule to $36257 x$ .

$\frac{36257^{0} x^{0}}{{(z^{8})}^{0}}$

Step 4

Simplify the numerator.

Anything raised to $0$ is $1$ .

$\frac{1 x^{0}}{{(z^{8})}^{0}}$

Anything raised to $0$ is $1$ .

$\frac{1 \cdot 1}{{(z^{8})}^{0}}$

Multiply $1$ by $1$ .

$\frac{1}{{(z^{8})}^{0}}$

Step 5

Simplify the denominator.

Multiply the exponents in ${(z^{8})}^{0}$ .

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

$\frac{1}{z^{8 \cdot 0}}$

Multiply $8$ by $0$ .

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

Anything raised to $0$ is $1$ .

$\frac{1}{1}$

Step 6

Divide $1$ by $1$ .

$1$