Question

if (m)n = 64,when m and n are positive integers,then find the value of (n)mn

Answer 1

A/C to question,
$m^n=64$ , 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
∴ $n^{mn}=6^{2\times6}$ = 6¹²

Case2 :- when you write 64 = 4³
Then, m = 4 and n = 3
∴$n^{mn}=3^{4\times3}=3^{12}$

Case 3 :- when you wirte 64 = 8²
Then,m = 8 and n = 2
∴$n^{mn}=2^{8\times2}=2^{16}$

Answer 2

Answer:

$n^{mn}=6^{12}$

Step-by-step explanation:

Given: $m^n=64$

To find: Value of $n^{mn}$

Clearly in given statement.

LHS is a exponential And RHS is a Number.

First we convert given number in exponential form.

Prime Factorization of 64 = 2 × 2 × 2 × 2 × 2 × 2 = $2^6$

So, We have

$m^n=2^6$

By comparing both sides,

we get

m = 2  and n = 6

So, $n^{mn}=6^{2\times6}=6^{12}$

Therefore, $n^{mn}=6^{12}$