Answer :

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.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

If 2x Karnataka Board - Mathematics Part II

Find the value ofKarnataka Board - Mathematics Part II

If x,y, <imKarnataka Board - Mathematics Part II

Find the value ofKarnataka Board - Mathematics Part II

The diameter of tKarnataka Board - Mathematics Part II

Suppose 3k</Karnataka Board - Mathematics Part II

If a7 Karnataka Board - Mathematics Part II

The number Karnataka Board - Mathematics Part II

The value of (3<sKarnataka Board - Mathematics Part II

Find the value ofKarnataka Board - Mathematics Part II