Question

Find the 499th digit in the expansion of (34128700)^249

Answer 1

The given expansion is : $(34128700)^{249}$

  = $(341287)^{249}\times (100)^{249}$

Now, $(100)^{249}$= 498 zeros on the right of 1.

$(341287)^{249}$ has 7 at it's unit digit.

As,  $7^{4}$ has 1 at it's unit digit.

249 = 62 × 4 + 1

$7^{249}=7^{62 \times 4 + 1}= 7 {\text{at it's unit digit.}}$

So, in the expansion of $(34128700)^{249}$ the 499th term is 7.