Evaluate (1+(1/100))^100

${(1 + (\frac{1}{100}))}^{100}$

Step 1

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

${(\frac{100}{100} + \frac{1}{100})}^{100}$

Step 2

Combine the numerators over the common denominator.

${(\frac{100 + 1}{100})}^{100}$

Step 3

Add $100$ and $1$ .

${(\frac{101}{100})}^{100}$

Step 4

Apply the product rule to $\frac{101}{100}$ .

$\frac{101^{100}}{100^{100}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{101^{100}}{100^{100}}$

Decimal Form:

$2.70481382 \dots$