Question

Four different numbers a,b,c,and d are chosen from the set {-1,-2,-3,-4,-5} .Find the largest possible value for the expression

Answer 1

\[\huge a^b+c^d\]

Answer 2

hmmm... interesting problem. my first thought is that b and d must be even so that both \(a^b\) and \(c^d\) are positive

Answer 3

so then problem reduces to finding maximum value of this expression:\[\frac{1}{a^2}+\frac{1}{b^4}\]with a and b drawn from the set {-1, -3, -5}

Answer 4

naturally we should go for -1 and -3.

Answer 5

-1 = b and -3 =a

Answer 6

exactly

Answer 7

I was /hoping/ that @Jonask would fill in the blanks :)

Answer 8

lol yes you made a good start
a=-3 and b=-1
since \[\left| a \right| \ge \left| b \right|\]

Answer 9

5 would yield a smaller result so not part of the solution

Answer 10

yup :)