Question

If x^y denotes x raised to the power y,then find last two digit of 1507^3381+1457^3757

Answer 1

Answer:

The last two digits are 64.

Explanation:

The given problem can be reduced to finding the last 2 digits.

Note that 57² ≡ 7² ≡ 49(mod100),

so that 57⁴ ≡ 7⁴ ≡ 49² ≡ 1(mod100).

Therefore,

1507³³⁸¹+1457^³⁷⁵⁷

= 7³³⁸¹ + 57³⁷⁵⁷ (mod 100)

= 7*(7⁴)⁸⁴⁵ + 57*(57⁴)⁹³⁹ (mod 100)

= 7 (1) + 57 (1)

= 7 + 57

= 64  last two digits

That's the final answer.

I hope its help you.