Several intervals can be combined into one region using the "set union" operation, ∪∪, which is represented as "u" in webwork. for example, [-2,0] u (8,inf) represents the points from −2−2 to 00 together with everything bigger than 8.

Write the set of points from  -6 to 0 but excluding  -4  and 0 as a union of intervals

First we take  the interval  -6 to 0. In that -4  and 0 are excluded.

So we split the interval -6 to 0.

Start with -6 and go up to -4. -4 is excluded so we break at -4. Also we use parenthesis for -4.

Interval becomes [-6,-4) . It says -6 included but -4 excluded.

Next interval starts at -4 and ends at 0. -4 and 0 are excluded so we use parenthesis not square brackets

(-4,0)

Now we take union of both intervals

[-6,-4) U (-4,0)  --- Interval from  -6 to 0 but excluding  -4  and 0

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation:

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