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:

2a⁶ x 6a⁷
(2 x 6)a^{(6 + 7)}
12a¹³

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 50mph \times 9h \)
450 miles

If the tiger has consumed 55 pounds of food in 5 days that's \( \frac{55}{5} \) = 11 pounds of food per day. The tiger needs to consume 121 - 55 = 66 more pounds of food to reach 121 pounds total. At 11 pounds of food per day that's \( \frac{66}{11} \) = 6 more days.

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

The equation for this sequence is:

a_n = a_n-1 + 4

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 + 4
a₆ = 17 + 4
a₆ = 21