Math Is Fun Forum

fayefaye

Member

Registered: 2007-08-11

Posts: 0

algebra exponents - which is greatest?

a. 2^(3^5)
b. (2^3)^5
c. 3^(2^5)
d. (3^2)^5
e. 5^(3^2)

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: algebra exponents - which is greatest?

Numbers increase veeery quickly with large exponents, so you want to have the biggest one you can here.
So the answer is a, as that gives

, which is massive.

HallsofIvy

Guest

Re: algebra exponents - which is greatest?

As Identity said, 2^(3^5) is "massive".  According to my calculator it is a 74 digit number!

  The other options, which do not have the exponents in increasing order, are:
b. (2^3)^5= 8^5= 32768
c. 3^(2^5)= 3^32= 1853020188851841
d. (3^2)^5=  9^5= 59049
e. 5^(3^2)= 5^9= 1953125
  But the important thing is what Identity said: it is not necessary to actually calculate the numbers to determine which is largest: just recognize that you want the exponent as large as possible.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: algebra exponents - which is greatest?

Also there is some log relationship multiplied if it is a close call depending on the base.
Like 3^x and 2^y.  Take the log(3) and log(2).
Their quotient might set the values for x and y for similar answers.
I'm just rambling from memory, so I might be wrong.

---

igloo myrtilles fourmis