Question

if m^n= 64, m and n are positive integer,find the value of n^m^n (2nd question of the worksheet)

Answer 1

Hi there!

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
$n^{mn}$=$6^{2 X 6}$=$6^{12}$

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

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

Hope it helps..
PS: pls make it the brainliest