Verified answer

Howdy Jennifer B, & I sure hope all is well. :)

As for your questions,

Part 1)

First, realize that the cubic root of something, is that thing raised to the power of 1/3, or 0.333 etc.

So the original expression can now be re-written as:

3√64/1000 = [64^(1/3)]/[1000^(1/3)]

Simplifying yields:

3√64/1000 = 4/10 = 0.4

Part 2)

3√-- 27X^6

To make it easier, break it down into steps:

The cubic root of a product, is the product of the cubic roots of the things being multiplied. I.e. (ab)^(1/3) = [a^(1/3)][b^(1/3)]

So the original expression can now be re-written as:

3√-- 27X^6 = [(-- 27)^(1/3)][(X^6)^(1/3)]

When raising something to a series of powers, such (a^b)^c, then you raise that thing to the product of the powers: (a^b)^c = a^(bc).

So we now have:

3√-- 27X^6 = (-- 3)[X^(6/3)]

3√-- 27X^6 = (-- 3)(X^2)

I sure hope that was as clear & as helpful as you needed it to be. :) Good luck, take care, & have a great day & a great weekend. :)

Cheers! :)

Cube root means instead of the number being multiplied by itself once, it's multiplied by itself twice. The answer to the first is 4/10. 4*4*4 = 64 and 10*10*10 = 1000. The second is more difficult but the same principle. The cube root of a negative is always a negative. So the cube root of -27 is -3. -3*-3 = 9 and 9*-3 = -27. The cube root of x^6 I'm not sure about... I can do cube roots of numbers pretty good but the variables always confused me. I think the answer is x^2. I'm not totally sure about the x^6 though, but I know the others are correct.

Hope that helped! : )

1. 4*4*4 = 64 and 10*10*10 = 1000

Just remember that that statement can be rewritten as (3√64)/(3√1000), so the answer is 4/10.

2. A root of a number can also be rewritten like this n√x = x^1/n, so you can take that 3 and rewrite it as an exponent of 1/3, like this:

-27^1/3x^(6 * 1/3)

=-27^1/3x^2

=-3x^2

(64/1000)^(1/3)=4/10=2/5

(-27x^6)^(1/3)

-3x^2