Evaluate (1+1000^-1)^1000

${(1 + 1000^{- 1})}^{1000}$

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

${(1 + \frac{1}{1000})}^{1000}$

Write $1$ as a fraction with a common denominator.

${(\frac{1000}{1000} + \frac{1}{1000})}^{1000}$

Combine the numerators over the common denominator.

${(\frac{1000 + 1}{1000})}^{1000}$

Add $1000$ and $1$ .

${(\frac{1001}{1000})}^{1000}$

Apply the product rule to $\frac{1001}{1000}$ .

$\frac{1001^{1000}}{1000^{1000}}$