Question

if m and n are two natural number no and m Power n = 32 then n power mn 8s​

Answer 1

Answer:

It is given that m and n are two natural numbers such that mnmn=32 and have to find a value of nmnnmn. Since, we have two variables m and n, but have only one equation, we have to think of a different way to solve the problem. Since, we have to represent in the form of mnmn, we list down the divisors of 32. We have,

32 = 2×2×2×2×22×2×2×2×2

Thus, we can write 32 = 2525. (m=2, n=5)

Another solution which exists is 32 = 321321 (trivial solution). Here, m = 32, n=1.

Thus, there are two cases.

Case 1: m=2, n=5

Now, we have nmnnmn = 52×552×5 = 510510= 9765625

Case 2: m=32, n=1

Now, we have nmnnmn = 132×1132×1 = 132132= 1

Thus, we have two values of nmnnmn. These are 1 and 9765625.