Question

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

Answer 1

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

Answer 2

(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