Question

Choose the correct simplification of the expression a^7b^8/a^4b^4

A: a^11b^12
B: a^3b^4
C: 1/a^3b^4
D: 1/a^3b^2

Answer 1

Move .Use the power rule to combine exponents.Add and to get .Move .Use the power rule to combine exponents.Add and to get .
Like...so it would get you:
(a7b12)(a4b8)(a7b12)(a4b8) Move a4a4 .a4a7b12b8a4a7b12b8 Use the power rule aman=am+naman=am+n to combine exponents.a4+7b12b8a4+7b12b8 Add 44 and 77 to get 1111 .a11b12b8a11b12b8 Move b8b8 .a11(b8b12)a11(b8b12) Use the power rule aman=am+naman=am+n to combine exponents.a11b8+12a11b8+12 Add 88 and 1212 to get 2020 .a11b20a11b20

So for the simplification, go with A, bc a11b8+12a11b8+12 looks the closest youre gong to get to whats there so A a^11b^12 is yours.
~~~~Hope this helps!

Answer 2

The answer is B: a^3b^4

Proof:
Simplify the following:
(a^7 b^8)/(a^4 b^4)

Combine powers. (a^7 b^8)/(a^4 b^4) = a^(7 - 4) b^(8 - 4):
a^(7 - 4) b^(8 - 4)

7 - 4 = 3:
a^3 b^(8 - 4)

8 - 4 = 4:
Answer: a^3 b^4

PS: I just wish that you put the equation down as it's intended i.e.
a^7b^8/a^4b^4 is not the same as (a^7b^8)/(a^4b^4)