What is 7 to the power 4, modulo 5?

Mathematics

ScanSolve AI Answer

Answer

74(mod5)7^4 \pmod{5} is 1.

Step-by-step solution

4 steps

Here's how to calculate it:

  1. Reduce the base modulo 5

    7≡2(mod5)7 \equiv 2 \pmod{5}

  2. Substitute the reduced base into the expression

    74≡24(mod5)7^4 \equiv 2^4 \pmod{5}

  3. Calculate the power

    24=162^4 = 16

  4. Reduce the result modulo 5

    16÷5=316 \div 5 = 3 with a remainder of 1.
    So, 16≡1(mod5)16 \equiv 1 \pmod{5}

    Therefore, 74(mod5)=17^4 \pmod{5} = 1.

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