Exponents & Roots Practice

GRE Quant Problem Solving
1

Hi all,

First time poster here. In the last problem of the exponents and roots practice: (Exponents and Roots Practice - GregMat). I understand the strategy and writing out the pattern. What I don’t understand is how Greg determines that the 7^240 will match the 4th position in the pattern (0), and 241 will then match the 5th position(0)? I had thought that 241 would match, the 11th position in the pattern (4)?

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Thank you!

2
7^1={07} \\ 7^2=49\\ 7^3=343\\ 7^4=2401\\ 7^5=16807\\ 7^6=117649

Now, we can see that the pattern is repeating itself after four powers of 7. Thus, we will divide 241 by 4. Now, 240 goes evenly into 4 (.i.e. remainder 0), so, 241 will have the same tens digit as 7^1 as the cycle repeats every 4 power of 7.

3

Thank you so much for the perfect explanation!