Question

use a calculator to approximate the number below.
$10.1^{5}$
$10.1^{5}\approx\square$ (round to four decimal places as needed.)

Explanation:

Step1: Understand the exponentiation

We need to calculate \(10.1^5\), which means multiplying 10.1 by itself 5 times: \(10.1\times10.1\times10.1\times10.1\times10.1\).

Step2: Calculate step - by - step

First, calculate \(10.1\times10.1 = 102.01\).
Then, multiply the result by 10.1: \(102.01\times10.1=102.01\times(10 + 0.1)=102.01\times10+102.01\times0.1 = 1020.1+10.201 = 1030.301\).
Next, multiply \(1030.301\times10.1\): \(1030.301\times10.1 = 1030.301\times10+1030.301\times0.1=10303.01 + 103.0301=10406.0401\).
Finally, multiply \(10406.0401\times10.1\): \(10406.0401\times10.1=10406.0401\times10 + 10406.0401\times0.1=104060.401+1040.60401 = 105101.00501\).

Answer:

\(10.1^{5}\approx105101.0050\) (rounded to four decimal places)