2m5n (m, n N) ends with ………..

2m5n = 2m – 1 × 5n – 1 × 2 × 5 = 2m – 1 × 5n – 1 × 10(m, n N so (m – 1), (n – 1) N – {0} )2m × 5n ends with 0

Q43 of 128 Page 25

2^m5ⁿ (m, n N) ends with ………..

2^m5ⁿ = 2^{m – 1} × 5^{n – 1} × 2 × 5 = 2^{m – 1} × 5^{n – 1} × 10

(m, n N so (m – 1), (n – 1) N – {0} )

2^m × 5ⁿ ends with 0

The decimal expansion of will terminate after …….. digits.

5ⁿ (n N) ends with ………..

represents

(5k + 1)² leaves remainder ……….. on dividing by 5.