To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

5a⁷ + 6a⁷
(5 + 6)a⁷
11a⁷

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

-a² x 2a⁴
(-1 x 2)a^{(2 + 4)}
-2a⁶

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [20, 40, 60, 80] making 20 the smallest multiple 4 and 10 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{8 x 5}{4 x 5} \) - \( \frac{3 x 2}{10 x 2} \)

\( \frac{40}{20} \) - \( \frac{6}{20} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{40 - 6}{20} \) = \( \frac{34}{20} \) = 1\(\frac{7}{10}\)

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.

To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{30\sqrt{14}}{6\sqrt{2}} \)
\( \frac{30}{6} \) \( \sqrt{\frac{14}{2}} \)
5 \( \sqrt{7} \)