Simplify ((4^0)^-2)/(4^2)

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

Step 1

Move ${(4^{0})}^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Simplify the denominator.

Raise $4$ to the power of $2$ .

$\frac{1}{16 {(4^{0})}^{2}}$

Multiply the exponents in ${(4^{0})}^{2}$ .

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

$\frac{1}{16 \cdot 4^{0 \cdot 2}}$

Multiply $0$ by $2$ .

$\frac{1}{16 \cdot 4^{0}}$

Anything raised to $0$ is $1$ .

$\frac{1}{16 \cdot 1}$

Step 3

Multiply $16$ by $1$ .

$\frac{1}{16}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{16}$

Decimal Form:

$0.0625$