Simplify (-4b^-2)^0

${(- 4 b^{- 2})}^{0}$

Step 1

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

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

Step 2

Combine $- 4$ and $\frac{1}{b^{2}}$ .

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

Step 3

Move the negative in front of the fraction.

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

Step 4

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

Apply the product rule to $- \frac{4}{b^{2}}$ .

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

Apply the product rule to $\frac{4}{b^{2}}$ .

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

Step 5

Simplify the expression.

Anything raised to $0$ is $1$ .

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

Multiply $\frac{4^{0}}{{(b^{2})}^{0}}$ by $1$ .

$\frac{4^{0}}{{(b^{2})}^{0}}$

Anything raised to $0$ is $1$ .

$\frac{1}{{(b^{2})}^{0}}$

Step 6

Simplify the denominator.

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

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

$\frac{1}{b^{2 \cdot 0}}$

Multiply $2$ by $0$ .

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

Anything raised to $0$ is $1$ .

$\frac{1}{1}$

Step 7

Divide $1$ by $1$ .

$1$