SOLUTION: what is 512^-1/3 convert into radical notation

Question 717542: what is 512^-1/3 convert into radical notation

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

If you have trouble with negative and/or fractional exponents, I have found that it can be helpful to factor the exponent in a special way:

If the exponent is negative, factor out -1.
If the exponent is a fraction and its numerator is not 1, then factor out the numerator.

Using this on your expression...
1. The exponent is negative so we factor out -1:

2. The exponent is a fraction. But its numerator is a 1 so we do nothing.

Once the exponent is factored this way, each factor tells you an operation to perform:

A factor of -1 in the exponent means we should find a reciprocal.
A factor that is a fraction (with a numerator of 1) means find a root of the kind specified by the denominator.
If there is another factor it will be a positive whole number which means what it usually means.

And these operations can be done in any order! So choose an order that looks easier.

So for:

we will find a reciprocal and find a cube root. Which should we start with? If we start with the reciprocal we get a fraction (since the reciprocal of 512 is 1/512). Then we would be finding a cube root of a fraction. Or we could start with the cube root and then find the reciprocal. This second path looks easier to me.

After a little effort we should be able to figure out that so the cube root of 512 is 8. And the reciprocal of 8 is 1/8. So:

Since 512 was a perfect cube we never really needed radical notation. But we could use it anyway:

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