Question

If a, m, n are positive integers, then find the value of { √ √ }



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Answer 1

Answer:

A/C to question,

m^n=64m

n

=64 , 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

∴ n^{mn}=6^{2\times6}n

mn

=6

2×6

= 6¹²

Case2 :- when you write 64 = 4³

Then, m = 4 and n = 3

∴n^{mn}=3^{4\times3}=3^{12}n

mn

=3

4×3

=3

12

Case 3 :- when you wirte 64 = 8²

Then,m = 8 and n = 2

∴n^{mn}=2^{8\times2}=2^{16}n

mn

=2

8×2

=2

16

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