Evaluate (1+500^-1)^500

${(1 + 500^{- 1})}^{500}$

Step 1

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

${(1 + \frac{1}{500})}^{500}$

Step 2

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

${(\frac{500}{500} + \frac{1}{500})}^{500}$

Step 3

Combine the numerators over the common denominator.

${(\frac{500 + 1}{500})}^{500}$

Step 4

Add $500$ and $1$ .

${(\frac{501}{500})}^{500}$

Step 5

Apply the product rule to $\frac{501}{500}$ .

$\frac{501^{500}}{500^{500}}$