how do I turn (1/64)^-1/3 into a radical?
I also need to know how to do the same thing with:
x^3/4 * x^ 1/2
- 1 decade agoFavorite Answer
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).
- 1 decade ago
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!Source(s): me, 12th grade seniorrrr
- Anonymous1 decade ago
get it a degree in politics and send it off to DC.