# How many digits a

23 × 54 × 205 = 23 × 54 × (4× 5)5

Using For a 0 and b 0, and integer m,

(a × b)m = am × bm

23 × 54 × 205 = 23 × 54 × 45× 55

23 × 54 × 205 = 23 × 54 × (22 )5× 55

Using third law of exponents, If a ≠0 is a number and m, n are integers, then (am)n= amn

23 × 54 × 205 = 23 × 54 × 210× 55

Using For any a 0, and integers m, n,

am × an = am+n

23 × 54 × 205 = 23+10 × 54+5

23 × 54 × 205 = 213 × 59

We know that 2× 5 = 10

So, 23 × 54 × 205 = (29 × 59)× 24

23 × 54 × 205 = 109 × 16

23 × 54 × 205 =16000000000

Hence, there are 11 digits in the given number.

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