Question

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

(2^7⋅2^5)/16

Answer 1

`(2^(7) . 2^(5) )/(16)` = 256

Explanation:

The given expression is
`(2^(7) . 2^(5) )/(16)`

Now, the Laws of Exponents state that

1.
`a^(x).a^(y)   = a^((x+ y))`

2.
`(a^(x) )/(a^(y) )  = a^((x-y))`

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

`(2^(7) . 2^(5) )/(16)` =
`(2^(7 + 5)  )/(16)`

Now,
`16 = 2^(4)`

So, substituting 16 with it, we get

`(2^(7 + 5)  )/(16)` =
`(2^(12)  )/(2^(4))`

=
`2^(12 - 4)  = 2^(8)`

Simplyimng this further, we get

`2^(8) = 256`

⇒
`(2^(7) . 2^(5) )/(16)` = 256