Question

2^m×2^n=2^-6 and determine which values of m and n are solutions are solutions

1.m=3,n=-9
2.m=-2,n=3
3.m=-4,n=2
4.m=-2,n=-3

Answer 1

(2^m)(2^n) = 2^(-6)

(2^m)(2^n) = 2^(m+n) = 2^(-6)

Since 2 = 2 their exponent are equal:
m+n = - 6

if m = 3 and n = -9 then m+n = 3-9 = -6
And tge answer is 1. m=3 & n = -9

Answer 2

remember

`(x^m)(x^n)=x^(m+n)`
and
if
`x^m=x^n` where x=x then m=n
so

`(2^m)(2^n)=2^(m+n)=2^(-6)`
so
m+n=-6
so test the options

first one works
2nd ones doesn't
3rd one doesn't
4th one doesnt'

answer is first option, m=3 and n=-9