Answer:
[tex]\frac{2^{7} . 2^{5} }{16}[/tex] = 256
Step-by-step explanation:
The given expression is [tex]\frac{2^{7} . 2^{5} }{16}[/tex]
Now, the Laws of Exponents state that
1. [tex]a^{x}.a^{y} = a^{(x+ y)}[/tex]
2. [tex]\frac{a^{x} }{a^{y} } = a^{(x-y)}[/tex]
Now, simplifying the expression using the two laws, we get
[tex]\frac{2^{7} . 2^{5} }{16}[/tex] = [tex]\frac{2^{7 + 5} }{16}[/tex]
Now, [tex]16 = 2^{4}[/tex]
So, substituting 16 with it, we get
[tex]\frac{2^{7 + 5} }{16}[/tex] = [tex]\frac{2^{12} }{2^{4}}[/tex]
= [tex]2^{12 - 4} = 2^{8}[/tex]
Simplyimng this further, we get
[tex]2^{8} = 256[/tex]
⇒ [tex]\frac{2^{7} . 2^{5} }{16}[/tex] = 256
