if f(x) = x 2/3, waht is the value of f(8) / f(3)?

Answer 1

If you mean

f(x) = x^(2/3), then

f(8) / f(3) = [8^(2/3)] / [3^(2/3)], which reduces to

4 / [3^(2/3)]

We can rationalize the denominator by multiplying top and bottom by 3^(1/3), to get

[4*3^(1/3)] / 3, which becomes

(4/3) (3^(1/3))

Answer 2

If f(x) = x to the two-thirds power, then f(8) = 4 (because x^2/3 is the same as (the cube root of 8) squared [= 2^2 = 4] or the cube root of (8 squared) [= cube root of 64 = 4]. Easy enough!

However, f(3) = (3^2)^1/3 = 9^1/3 = cube root of 9. Messier.

So f(8)/f(3) = 4 / 9^1/3. Since standard form requires we do not leave a fractional power in the divisor, multiply by one in the form of 9^2/3 / 9^2/3 and we have 4 * 9^2/3 / 9 = 4/9 * 9^2/3 and since 9^2/3 = 81^1/3 = 3^1/3 * 27^1/3 = 3*3^1/3 we substitute and get: 4 / 9 * 3 * 3^1/3 = 12/9 * 3^1/3 = 4/3 * 3^1/3. Which also equals about 1.922999427.

Answer 3

This is very very basic functions.
f(8) means "the value of f(x) when x=8". so just plug 8 into that expression you have on the left. The number you end up with is called f(8).
f(3) means x=3. so do the same thing, but with 3. this number is called f(3).

divide f(8) by f(3). hooray!

Answer 4

f(8)/f(3) is 16/6

Answer 5

Please check your book and be specific > clarify what "x 2/3" means > do you mean (2/3)(x) Or x^2/3 (x raised to the power of 2/3)?