Rowan has two pieces of cable, one 15 feet long and the other 12 feet long. For a science project he wants to cut them up to produces pieces of cable that are all the same length, with no cable left over. What is the greatest length, in feet, that he can make them?

The greatest length she can cut to have equal length in all the cables, without a left over is 3 feet each

Step-by-step explanation:

in order to solve this, we treat the length of each cable as separate numbers for which we find the highest common factor, since we are told that they must all be of the same length. The highest common factor of two whole numbers, is the highest number which completely divides both number without a remainder. The highest common factor is found as follows:

Factors of 12 are : 1, 2, 3, 4, 6, and 12

factors of 15 are : 1, 3, 5, and 15

from the above, the highest factor that is common to both numbers is 3.

Therefore, if both cables are cut into 3 feet each, , a total of 9 pieces of cables (4 from the 12 feet cable and 5 from the 15 feet cable) of equal length will be obtained without any remainder.

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:

the answer is 62.8 cubic units