Question

A and b are positive integers and a-b=2 ... Evaluate the following:

a) 2^a/2^b
b) 5^a/5^b
c) 4^0.5a/2^b

Answer 1

c=4

Explanation:

becus rsm said it was correct

Answer 2

A) = 4.

B) = 25.

C) = 4.

Explanation:

We are given that a and b are positive integers and that:

`a-b=2`

And we want to evaluate the following expressions.

Expression A)

We have:

`\displaystyle (2^a)/(2^b)`

This is equivalent to:

`=2^a/ 2^b`

Therefore:

`=2^(a-b)`

Substitute and evaluate:

`=2^((2))=4`

Expression B)

We have:

`\displaystyle (5^a)/(5^b)`

This is equivalent to:

`=5^(a-b)`

Again, substitute and evaluate:

`=5^((2))=25`

Expression C)

Lastly, we have:

`\displaystyle (4^(0.5a))/(2^b)`

Note that 4 = 2². Hence:

`=\displaystyle ((2)^(2(0.5a)))/(2^b)`

Simplify:

`=\displaystyle (2^a)/(2^b)`

Using the previous result:

`=4`