Answer:
We have:
[tex]\frac{3^{a+b} }{3^{a-b} }=81=3^{4} \\\\=> 3^{a+b}=3^{4}.3^{a-b} \\\\<=> 3^{a+b}=3^{a-b+4}\\\\=> a + b = a-b+4\\\\<=> 2b=4\\\\<=>b=2[/tex]
we also have:
[tex]\frac{2^{2a+b} }{2^{2b-a} }=128=2^{7}\\\\<=>2^{2a+b}=2^{7}.2^{2b-a}\\\\<=>2^{2a+b}=2^{2b-a+7}\\\\=>2a+b=2b-a+7\\\\<=>3a=b+7\\\\\\[/tex]
with b = 2 => 3a = 9 => a = 3
with a = 3; b = 2 => a + b = 5
Step-by-step explanation:
