Question

Simplify and express the following in exponential form:

`(2^3 xx 3^4 xx 4)/(3 xx 32)`

Answer 1

`(2^3 xx 3^4 xx 4)/(3 xx 32) = (2^3 xx 3^4 xx 2 xx 2)/(3 xx 2 xx 2 xx 2 xx 2 xx 2)`

= `(2^3 xx 3^4 xx 2^2)/(3 xx 2^5)`

= `(2^(3  +  2)  xx 3^4)/(3 xx 2^5)`       ...(∵ a^m × aⁿ = a^{m + n})

= `(2^5 xx 3^4)/(3 xx 2^5)`

= 2^{5 - 5} × 3^{4 - 1}         ...(∵ a^m ÷ a^m = a^{m - n})

= 2⁰ 3³

= 1 × 3³

= 3³