Simplify (2^0a^4b^2)^-2

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

Step 1

Anything raised to $0$ is $1$ .

${(1 a^{4} b^{2})}^{- 2}$

Step 2

Multiply $a^{4}$ by $1$ .

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

Step 3

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

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

Step 4

Simplify the denominator.

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

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

Multiply the exponents in ${(a^{4})}^{2}$ .

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

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

Multiply $4$ by $2$ .

$\frac{1}{a^{8} {(b^{2})}^{2}}$

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

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

$\frac{1}{a^{8} b^{2 \cdot 2}}$

Multiply $2$ by $2$ .

$\frac{1}{a^{8} b^{4}}$