We should know that 8 = 2. To see how this is equivalent to 8% = 2 we can solve the equation 8" - 2. To do this, we can rewrite the equation as:
(2")" = 2
How can we now use this equation to see that 8 1/3=2

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Step-by-step explanation:

By the rules of exponents, ...

  (a^b)^c = a^(bc)

__

  (2^3)^n = 2^1 . . . . . given

  2^(3n) = 2^1 . . . . . . rule of exponents

  3n = 1 . . . . . . . . . . . equate exponents

  n = 1/3 . . .  . . . . . . . divide by 3

Recognize that 2^3 = 8, and 2^1 = 2, then substitute into the given equation:

  8^(1/3) = 2

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).