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

\( \frac{10\sqrt{42}}{5\sqrt{6}} \)
\( \frac{10}{5} \) \( \sqrt{\frac{42}{6}} \)
2 \( \sqrt{7} \)

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

\( \frac{a^7}{3a^2} \)
\( \frac{1}{3} \) a^{(7 - 2)}
\(\frac{1}{3}\)a⁵

If the tiger has consumed 36 pounds of food in 6 days that's \( \frac{36}{6} \) = 6 pounds of food per day. The tiger needs to consume 78 - 36 = 42 more pounds of food to reach 78 pounds total. At 6 pounds of food per day that's \( \frac{42}{6} \) = 7 more days.

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [40, 80] making 40 the smallest multiple 8 and 10 share.

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

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

\( \frac{40}{40} \) - \( \frac{8}{40} \)

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

\( \frac{40 - 8}{40} \) = \( \frac{32}{40} \) = \(\frac{4}{5}\)

To raise a term with an exponent to another exponent, retain the base and multiply the exponents: