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    What is the value of 1013101^31013​?
    Question

    What is the value of 1013101^3​?

    A.

    1020301

    B.

    1030201

    C.

    1030301

    D.

    1020201

    Correct option is C

    Given:

    The expression is 1101301^3​​

    Solution:

    1013=101×101×101=1030301101^3 = 101 \times 101 \times 101= 1030301 

    By algebraic  identity  

    (a+b)3=a3+b3+3ab(a+b)(a+b)^3 = a^3 + b^3 + 3ab(a+b) 

    Solution: 

    (101)3=(100+1)3=(100)3+(1)3+3×100×1(1+100)=1000000+1+300+30000(101)^3 = (100 +1)^3 = (100)^3 + (1)^3 + 3\times 100 \times 1(1+100) \\ = 1000000+ 1+ 300 + 30000​​

    = 1030301

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