Math help please?

2017-12-27 1:33 am
How many pairs of integers (a, b) satisfy the equation a^b=1296?

回答 (3)

2017-12-27 1:42 am
1296 = 2⁴ × 3⁴
Hence, 1298 = 6⁴ = 36² = 1296¹

There are 3 pairs of integers (a, b) satisfy the equation aᵇ = 1296, i.e.
(6, 4), (36, 2) and (1296, 1)
2017-12-27 1:43 am
 
1296 = 6^4
1296 = (−6)^4
1296 = 6^(2*2) = (6^2)^2 = 36^2
1296 = (−36)^2
1296 = 1296^1

5 integer solutions: (6,4), (−6,4), (36,2), (−36,2), (1296,1)
2017-12-27 3:03 am


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