SOLUTION: How many pairs of integers (a,b) satisfy the equation {{{ab^a}}} = 648? CC11F #10

Question 1209405: How many pairs of integers (a,b) satisfy the equation = 648?
CC11F #10
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

The only prime factors of 648 are 2 and 3.

a is an exponent in the expression; the exponents in the prime factorization of 648 are 3 and 4. That means a can only be 1, 2, or 3.

(1) a=1

first solution: (a,b) = (1,648)

(2) a=2

or

second and third solutions: (a,b) = (2,18) and (a,b) = (2,-18)

(3) a=3

fourth solution: (a,b) = (3,6)

ANSWER: 4 pairs of integer (a,b) satisfy the equation ab^a = 648

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