A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).

To subtract these radicals together their radicands must be the same:

8\( \sqrt{18} \) - 9\( \sqrt{2} \)
8\( \sqrt{9 \times 2} \) - 9\( \sqrt{2} \)
8\( \sqrt{3^2 \times 2} \) - 9\( \sqrt{2} \)
(8)(3)\( \sqrt{2} \) - 9\( \sqrt{2} \)
24\( \sqrt{2} \) - 9\( \sqrt{2} \)

Now that the radicands are identical, you can subtract them:

If the tiger has consumed 40 pounds of food in 4 days that's \( \frac{40}{4} \) = 10 pounds of food per day. The tiger needs to consume 90 - 40 = 50 more pounds of food to reach 90 pounds total. At 10 pounds of food per day that's \( \frac{50}{10} \) = 5 more days.

The equation for this sequence is:

a_n = a_n-1 + 2(n - 1)

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 2(6 - 1)
a₆ = 21 + 2(5)
a₆ = 31

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:

7a³ + 8a³
(7 + 8)a³
15a³