Question

How many ways can the product a² b³ c⁴ be expressed without exponents?

Answer 1

The given term is a²b³c⁴

The factors are a, b, c

Number of a’s = 2

Number of b’s = 3

Number of c’s = 4

a²b³c⁴ = a × a × b × b × b × c × c × c × c

Total number of factors in the product = 9

Number of ways the product can be expressed without exponents

= `(9!)/(2! xx 3! xx 4!)`

= `(9 xx 8 xx 7 xx 6 xx 5 xx 4!)/(2! xx 3! xx 4!)`

= `(9 xx 8 xx 7 xx 6 xx 5)/(2 xx 1 xx 3 xx 2 xx 1)`

= 9 × 4 × 7 × 5

= 1260