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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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