Question

Showing step-by-step explanation, find the number of digits in

${3}^{12} \times {2}^{8}$

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Answer 1

Solution:-

=> 3¹² × 2^8

=> 3^(6×2) × 2^(4×2)

=> (3^6 × 2^4)^2

=> [ 3^(3×2) × 2^(2×2)]^2

=> ( 3^3 × 2^2)^4

=> ( 81 × 4)^4

=> 324^4

=> 11, 019, 960, 576.

Hence,

3^12 × 2^8 Consists of 11 Digit Numbers.

Answer 2

${3}^{12} \times {2}^{8}$

= (3³ × 2²)⁴

= (81 × 4)⁴

= (324)⁴

= (300 + 24)⁴

We have to find digits only, so just apply formula.

= {(300+24)²}²

= (90000 + 576 + 14400)²

Simply , (300+24)² has 6 digits.

= (324)⁴ is approx to (10^6)²( 104976)²

= so 324⁴ has 11 digits.

How I guess :p

= (100000)² = (10000000000)

11 digits.