Solve Easy Math Problem: Remainder of 6x7^32 + 17x9^45 Divided By 5

[dgentile]

Homework Statement

What is the remainder when 6 x 7^32 + 17 x 9^45 is divided by 5?

^ symbol just means exponent so like. 7 to the 32 power.

Homework Equations

I don't know how to convert to standard form from scientific notation on my calculator

I don't know how to add the numbers when they aren't in standard form

The Attempt at a Solution

6 x 7^32 = 6.63 e27
+
17 x 9^45 = 1.48 e44

6.63 e27 + 1.48 e44 = ? ? /5 remainder?

 

[Tedjn]

That is not a good way to go about finding the remainder when a number is divided by 5. In this case, division by 5 is special in that you can tell what the remainder is from the units digit of the number. For example, if the units digit is 3 or 8, we know that the remainder when divided by 5 is 3.

Putting such a huge calculation into the calculator gives you an approximation of the number in scientific notation. 6.63e27 + 1.48e44 is approximately 1.48e44, and it gives you the leading 3 digits of a 45 digit number. You need the last digit, so this does not help.

Instead, one way to do this problem is to see if you can figure out what the last digit of this huge product is. Perhaps there is a pattern to the last digit in the powers of 7 or the powers of 9 that can help you out.

There are also other related ways to do this question that require even less calculation, but the way I described is a good way to find a solution.