Simplify ((4^-6)/(4^2))^4

${(\frac{4^{- 6}}{4^{2}})}^{4}$

Step 1

Move $4^{- 6}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{1}{4^{2} \cdot 4^{6}})}^{4}$

Step 2

Multiply $4^{2}$ by $4^{6}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{1}{4^{2 + 6}})}^{4}$

Add $2$ and $6$ .

${(\frac{1}{4^{8}})}^{4}$

Step 3

Raise $4$ to the power of $8$ .

${(\frac{1}{65536})}^{4}$

Step 4

Apply the product rule to $\frac{1}{65536}$ .

$\frac{1^{4}}{65536^{4}}$

Step 5

One to any power is one.

$\frac{1}{65536^{4}}$

Step 6

Raise $65536$ to the power of $4$ .

$\frac{1}{18446744073709600000}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{18446744073709600000}$

Decimal Form:

$5.42101086 \cdot 10^{- 20}$