Question:The ages of A and B differ by 16 years. If 6 years ago, the elder one be 3 times as old as the younger one, find their present ages.
Let A's age = x & B's age = (x + 16) 3 (x - 6) = (x + 16 -6) or x = 7 `:.` Mother's present age = (4x + 7) = 35 years.
Question:`81^(3/4)`
`(3^4)^(3/4)` = `3^(4 xx 3/4)` =`3^3` = 27
Question:`(1/64)^(-5/6)`
`(1/64)^(-5/6)` =`64^(5/6)` =`(2^6)^(5/6)` =`2^(6 xx 5/6)` =`2^5` =32
Question:`256^(-1/4`
`256^(-1/4)` =`(1/256)^(1/4)` =`[(1/4)^4]^(1/4)` =`(1/4)^(4 xx 1/4)` =`1/4`
Question:`(x^b/x^c)^ ((b^2 + c^2 + bc))` x `(x^c/x^a)^ ((c^2 + a^2 + ca))` x `(x^a/x^b)^ ((a^2 + b^2 + ab))`
=`(x^(b - c))^((b^2 + c^2 + bc))` x `(x^(c - a))^((c^2 + a^2 + ca))` x `(x^(a - b))^((a^2 + b^2 + ab))` =`x^((b - c)(b^2 + c^2 + bc))` x `x^((c - a)(c^2 + a^2 + ca))` x `x^((a - b)(a^2 + b^2 + ab))` = `x^((b^3 - c^3))` x `x^((c^3 - a^3))` x `x^((a^3 - b^3))` =`x^((b^3 - c^3) + (c^3 - a^3) + (a^3 - b^3))` =`x^0` =1