If a number is in the form of 8¹⁰× 9⁷× 7⁸, find the total number of prime factors of the given number.

Question: If a number is in the form of 8¹⁰ × 9⁷ × 7⁸, find the total number of prime factors of the given number.

Solution:
If a number of the form x^a × y^b × z^c ...... and so on,
then total prime factors = a + b + c ..... and so on Where x, y, z, ... are prime numbers

The number 8¹⁰ × 9⁷ × 7⁸ can be written as (2³)¹⁰ × (3²)⁷ × 7⁸
= 2³⁰ × 3¹⁴ × 7⁸

Total number of prime factors = 30 + 14 + 8 = 52

∴ The total number of prime factors are 52