Question

Simplify and express the following in exponential form:

`(2^8 xxa^5)/(4^3 xx a^3)`

Answer 1

`(2^8 xxa^5)/(4^3 xx a^3) = (2^8 xx a^5)/((2 xx 2)^3 xx a^3)`

= `(2^8 xx a^5)/((2^2)^3 xx a^3)`

= `(2^8 xx a^5)/((2^(2  xx  3))xx a^3 )`         ...[∵ (a^m)ⁿ = a^mn]

= `(2^8 xx a^5)/(2^6 xx a^3)`

= 2^{8 - 6} × a^{5 - 3}       ...(a^m ÷ aⁿ = a^{m - n})

= 2² × a²

= (2 × a)²       ...[∵ a^m × b^m = (a × b)^m]

= (2a)²