easy exponents question.. x^A * x^ B = x ^(A+B) ??

[jsvlad]

simple exponents question. please see attached image.

top: 2^(A+B)
so 2a +2 on top
2a+2 - ab = 2a+2-a(a+2)
.. = 2a+2-aa-2a
= 2-a?
...





a=1, b= 3?
2*2^3 = 32..
2^4 / 2^6 = 1/2^2 = 1/4
must be 4..


q23 answer 4.

i can't do this without plugging in numbers. i was hoping somebody can clarify.

thanks..

 

[jsvlad]

Will you please post something that can be understood?

i apologize if it is unclear..
ill be more clear..
can somebody show me how to solve this problem without plugging in numbers!?

thanks!

 

[pka]

can somebody show me how to solve this problem without plugging in numbers!?

We know that \(\displaystyle b=a+2\)

\(\displaystyle \dfrac{2^a\cdot 2^b}{2^{ab}}=\dfrac{2^a\cdot 2^{a+2}}{2^{a(a+2)}}=\dfrac{2^{2a+2}}{2^{a^2+2a}}=\dfrac{2^2}{2^{a^2}}\)