How many digits are there in the number 2³ × 5⁴ × 20⁵?

2³ × 5⁴ × 20⁵ = 2³ × 5⁴ × (4× 5)⁵

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

(a × b)^m = a^m × b^m

⇒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 (a^m)ⁿ= a^mn

⇒2³ × 5⁴ × 20⁵ = 2³ × 5⁴ × 2¹⁰× 5⁵

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

a^m × aⁿ = a^m+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.