Question

if m^n=64 then n^mn=?

Answer 1

A/C to question,

, here m and n are positive integers.----(1)

First we should find out prime factors of 64

64 = 2 × 2 × 2 × 2 × 2 × 2

You can write , 64 = 2⁶ or 4³ or 8²

Case 1 :- when you write 64 = 2⁶

Compare with equation (1),

m = 2 and n = 6

∴ = 6¹²

Case2 :- when you write 64 = 4³

Then, m = 4 and n = 3

∴

Case 3 :- when you wirte 64 = 8²

Then,m = 8 and n = 2

∴