Could someone please help, by solving this and telling me how they did it?

Question

Find the indicated root, or state that the expression is not a real number.

- 3√-64
The - 3 is an exponent as is before the square root symbol.

Keep in mind his is a negative 3rd root of -64

The final answer will NOT be in fractional form, the only other option is that there is no solution.

Answer 1

64 = 2^6
So - 3√-64
= (-64)^(-1/3)
= (-1)^(-1/3) * (64)^(-1/3)
= 1/(-1)^(1/3) * (2^6)^(-1/3)
= 1/(-1) * 2^(-6/3)
= -1 * 2^-2
= -1 * 1/4
= - 1/4

Or, more simply,
(-64)^(-1/3)
= -(2)^[6*(-1/3)]
= -(2)^(-2)
= -1/4

I hope this helps!

Since you don't want the final answer is fractional form, then write it as -0.25! If you don't believe that this is correct, open up your calculator function on your computer. Click on VIEW and get the scientific calculator. Then put in -64 [x^y] (-1/3) and see what you get.

Answer 2

In real numbers, the square root of -64 does not exist. In fact, the square root of any negative number does not exist.

When seeking a square root of "X", you are looking for a number which, when multiplied by itself, will give "X".

If you multiply a positive number by itself (e.g., +2 times +2), the result is a positive value (+4).

If you multiply a negative number by itself (e.g., -2 times -2), the result is still a positive value (+4).

If X is a negative number, then you cannot find a real number that will give a negative number when multiplied. by itself.