# how do I turn (1/64)^-1/3 into a radical?

I also need to know how to do the same thing with:

100^-1/2

x^3/4 * x^ 1/2

Relevance

x^(1/3) is the same as the cube root of x.

x^(1/2) is the same as the square root of x.

x^(-1/3) is the same as 1 / (cube root of x).

x^(-1/2) is the same as 1 / (square root of x).

that is equivalent to:

1 / (3rd root of 1/64) = 1/ (1/4) = 4 (the "radical" would be like the square root sign (which is the 2nd root), but instead, it's the 3rd root.

a fractional exponent uses the root function, the negative sign reciprocates it (the 1/ (...) )

100 ^ -1/2 is equivalent to: 1 / (2nd or square root of 100) = 1/ 10 = 0.1

x^3/4 * x^ 1/2 is multiplying two functions with the same base (x). so since it is the same base, you can add the exponents and combine it into one function:

x^(3/4 +1/2) = x^(5/4) = (4th root of x)^5

or in english: 4th root of x to the fifth power

or equivalently: (4th root of (x^5))

even though the parantheses are different, it is the same expression.

hope this helps!