# Find the last two digits, without using a calculator, for this exponential expression

Many of you have probably been given mathematics homework assignments where you were supposed to answer the question without using a calculator. This is quite common in trigonometry where the student’s knowledge of the unit circle avoids the need of a calculator.

The following calculator buster question looks impossible to solve without a calculator, but there is a way to solve it without substituting the expression into your calculator.

The question is what are the last two digits in $11^{10}-9$ ?

The idea here is to write $11^{10}-9$  as  ${(10+1)}^{10}-1-8$

You will notice that the one’s digits will cancel simplifying matters. All that will be remaining is 8 subtracted from terms containing $10^{2}$ or greater. Therefore, subtracting 8 from a number that ends with 2 zeros forces last two digits to be 92 !

Math, like chess, exercises your brain and produces a sense of satisfaction when you figure something out!