Question

Use powers of 2 to perform each calculation without a calculator or other technology

Answer 1

Answer:

$\frac{2^{7} . 2^{5} }{16}$ = 256

Step-by-step explanation:

The given expression is $\frac{2^{7} . 2^{5} }{16}$

Now, the Laws of Exponents state that

1. $a^{x}.a^{y} = a^{(x+ y)}$

2. $\frac{a^{x} }{a^{y} } = a^{(x-y)}$

Now, simplifying the expression using the two laws, we get

$\frac{2^{7} . 2^{5} }{16}$  = $\frac{2^{7 + 5} }{16}$

Now,  $16 = 2^{4}$

So, substituting 16 with it, we get

$\frac{2^{7 + 5} }{16}$ = $\frac{2^{12} }{2^{4}}$

= $2^{12 - 4} = 2^{8}$

Simplyimng this further, we get

$2^{8} = 256$

⇒ $\frac{2^{7} . 2^{5} }{16}$ = 256