Question

Completely simplify the following expression:





8a8b12


8a4b2


9a4b2


9a12b35

Answer 1

Interpreting the expression as (8a^8 b^12)/(8a^4 b^2) · (9a^4 b^2)/(9a^12 b^35):

- Cancel constants: 8/8 = 1, 9/9 = 1.
- Simplify each power fraction:
- (a^8 b^12)/(a^4 b^2) = a^(8−4) b^(12−2) = a^4 b^10
- (a^4 b^2)/(a^12 b^35) = a^(4−12) b^(2−35) = a^(−8) b^(−33) = 1/(a^8 b^33)
- Multiply: a^4 b^10 · 1/(a^8 b^33) = a^(4−8) b^(10−33) = a^(−4) b^(−23) = 1/(a^4 b^23)

Answer: 1/(a^4 b^23), assuming a ≠ 0 and b ≠ 0.