Simplify ((-9p^(1/2)q)^0)^-1

${({(- 9 p^{\frac{1}{2}} q)}^{0})}^{- 1}$

Step 1

Multiply the exponents in ${({(- 9 p^{\frac{1}{2}} q)}^{0})}^{- 1}$ .

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

${(- 9 p^{\frac{1}{2}} q)}^{0 \cdot - 1}$

Multiply $0$ by $- 1$ .

${(- 9 p^{\frac{1}{2}} q)}^{0}$

Step 2

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

Apply the product rule to $- 9 p^{\frac{1}{2}} q$ .

${(- 9 p^{\frac{1}{2}})}^{0} q^{0}$

Apply the product rule to $- 9 p^{\frac{1}{2}}$ .

${(- 9)}^{0} {(p^{\frac{1}{2}})}^{0} q^{0}$

Step 3

Anything raised to $0$ is $1$ .

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

Step 4

Multiply ${(p^{\frac{1}{2}})}^{0}$ by $1$ .

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

Step 5

Multiply the exponents in ${(p^{\frac{1}{2}})}^{0}$ .

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

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

Multiply $\frac{1}{2}$ by $0$ .

$p^{0} q^{0}$

Step 6

Anything raised to $0$ is $1$ .

$1 q^{0}$

Step 7

Multiply $q^{0}$ by $1$ .

$q^{0}$

Step 8

Anything raised to $0$ is $1$ .

$1$