Question

Simplify : (i) `2^(2/3). 2^(1/5)` (ii) `(1/(3^3))^7` (iii) `(11^(1/2))/(11^(1/4))` (iv) `7^(1/2). 8^(1/2)`

Answer 1

(i) `2^(2/3).2^(1/5)`
As, `a^m.a^n = a^(m+n)`
`2^(2/3).2^(1/5)= 2^(2/3+1/5)=2^(13/15)`

(ii) `(1/3^3)^7`
As, `(a^m)^n)= a^(mn)`
`(1/3^3)^7 = 1/3^21 = 3^-21`

(iii) `(11^1/2)/(11^1/4)`
As, `a^m/a^n = a^(m-n)`
`(11^1/2)/(11^1/4)=11^(1/2-1/4) = 11^(1/4)`

(iv)`7^(1/2).8^(1/2)`
As, `a^m.b^m = (ab)^m`
`7^(1/2).8^(1/2) = (7.8)^1/2 = 56^(1/2)`