A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

If the tiger has consumed 64 pounds of food in 8 days that's \( \frac{64}{8} \) = 8 pounds of food per day. The tiger needs to consume 120 - 64 = 56 more pounds of food to reach 120 pounds total. At 8 pounds of food per day that's \( \frac{56}{8} \) = 7 more days.

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

2 + (3 + 5) ÷ 3 x 5 - 3²
P: 2 + (8) ÷ 3 x 5 - 3²
E: 2 + 8 ÷ 3 x 5 - 9
MD: 2 + \( \frac{8}{3} \) x 5 - 9
MD: 2 + \( \frac{40}{3} \) - 9
AS: \( \frac{6}{3} \) + \( \frac{40}{3} \) - 9
AS: \( \frac{46}{3} \) - 9
AS: \( \frac{46 - 27}{3} \)
\( \frac{19}{3} \)
6\(\frac{1}{3}\)

The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 80 are [1, 2, 4, 5, 8, 10, 16, 20, 40, 80]. They share 5 factors [1, 2, 4, 8, 16] making 16 the greatest factor 32 and 80 have in common.

To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.