Simplify 4a(0^(1/2))b^4(-b)^-7

$4 a (0^{\frac{1}{2}}) b^{4} {(- b)}^{- 7}$

Simplify the expression.

Rewrite $0$ as $0^{2}$ .

$4 a {(0^{2})}^{\frac{1}{2}} b^{4} {(- b)}^{- 7}$

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

$4 a \cdot 0^{2 (\frac{1}{2})} b^{4} {(- b)}^{- 7}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 a \cdot 0^{2 (\frac{1}{2})} b^{4} {(- b)}^{- 7}$

Rewrite the expression.

$4 a \cdot 0^{1} b^{4} {(- b)}^{- 7}$

Evaluate the exponent.

$4 a \cdot 0 b^{4} {(- b)}^{- 7}$

Multiply $4 a \cdot 0$ .

Multiply $0$ by $4$ .

$0 a b^{4} {(- b)}^{- 7}$

Multiply $0$ by $a$ .

$0 b^{4} {(- b)}^{- 7}$

Multiply $0$ by $b^{4}$ .

$0 {(- b)}^{- 7}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$0 \frac{1}{{(- b)}^{7}}$

Simplify the denominator.

Apply the product rule to $- b$ .

$0 \frac{1}{{(- 1)}^{7} b^{7}}$

Raise $- 1$ to the power of $7$ .

$0 \frac{1}{- b^{7}}$

Cancel the common factor of $1$ and $- 1$ .

Rewrite $1$ as $- 1 (- 1)$ .

$0 \frac{- 1 (- 1)}{- b^{7}}$

Move the negative in front of the fraction.

$0 (- \frac{1}{b^{7}})$

Multiply $0 (- \frac{1}{b^{7}})$ .

Multiply $- 1$ by $0$ .

$0 \frac{1}{b^{7}}$

Multiply $0$ by $\frac{1}{b^{7}}$ .

$0$