Answer:
A) = 4.
B) = 25.
C) = 4.
Step-by-step explanation:
We are given that a and b are positive integers and that:
[tex]a-b=2[/tex]
And we want to evaluate the following expressions.
Expression A)
We have:
[tex]\displaystyle \frac{2^a}{2^b}[/tex]
This is equivalent to:
[tex]=2^a\div 2^b[/tex]
Therefore:
[tex]=2^{a-b}[/tex]
Substitute and evaluate:
[tex]=2^{(2)}=4[/tex]
Expression B)
We have:
[tex]\displaystyle \frac{5^a}{5^b}[/tex]
This is equivalent to:
[tex]=5^{a-b}[/tex]
Again, substitute and evaluate:
[tex]=5^{(2)}=25[/tex]
Expression C)
Lastly, we have:
[tex]\displaystyle \frac{4^{0.5a}}{2^b}[/tex]
Note that 4 = 2². Hence:
[tex]=\displaystyle \frac{(2)^{2(0.5a)}}{2^b}[/tex]
Simplify:
[tex]=\displaystyle \frac{2^a}{2^b}[/tex]
Using the previous result:
[tex]=4[/tex]
