Simplify ((2^3m^4n^-1)/(p^2))^0

${(\frac{2^{3} m^{4} n^{- 1}}{p^{2}})}^{0}$

Move $n^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{2^{3} m^{4}}{p^{2} n})}^{0}$

Raise $2$ to the power of $3$ .

${(\frac{8 m^{4}}{p^{2} n})}^{0}$

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

Apply the product rule to $\frac{8 m^{4}}{p^{2} n}$ .

$\frac{{(8 m^{4})}^{0}}{{(p^{2} n)}^{0}}$

Apply the product rule to $8 m^{4}$ .

$\frac{8^{0} {(m^{4})}^{0}}{{(p^{2} n)}^{0}}$

Apply the product rule to $p^{2} n$ .

$\frac{8^{0} {(m^{4})}^{0}}{{(p^{2})}^{0} n^{0}}$

Simplify the numerator.

Anything raised to $0$ is $1$ .

$\frac{1 {(m^{4})}^{0}}{{(p^{2})}^{0} n^{0}}$

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

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

$\frac{1 m^{4 \cdot 0}}{{(p^{2})}^{0} n^{0}}$

Multiply $4$ by $0$ .

$\frac{1 m^{0}}{{(p^{2})}^{0} n^{0}}$

Anything raised to $0$ is $1$ .

$\frac{1 \cdot 1}{{(p^{2})}^{0} n^{0}}$

Multiply $1$ by $1$ .

$\frac{1}{{(p^{2})}^{0} n^{0}}$

Simplify the denominator.

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

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

$\frac{1}{p^{2 \cdot 0} n^{0}}$

Multiply $2$ by $0$ .

$\frac{1}{p^{0} n^{0}}$

Anything raised to $0$ is $1$ .

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

Anything raised to $0$ is $1$ .

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

Multiply $1$ by $1$ .

$\frac{1}{1}$

Divide $1$ by $1$ .

$1$